A Dynamical Systems Model of Port–Industry–City Co-Evolution Under Data Constraints

Abstract

This study develops a dynamical systems framework for analyzing the co-evolution of port–industry–city (PIC) systems, with particular attention to the data-limited contexts often encountered in developing coastal regions. The model integrates time-delay differential equations and stochastic disturbances to capture nonlinear behaviors such as investment cycles, policy lags, and external shocks. By introducing dimensionless indicators and dynamic parameter adjustment, the framework reduces dependence on extensive datasets and enhances cross-regional applicability. The Kribi Deep Seaport in Cameroon serves as an illustrative case, demonstrating how the approach can reveal emergent trajectories under alternative development regimes. Simulation results identify three distinct pathways: capital-driven expansion with risks of premature overinvestment, industrial clustering modes requiring coordinated urban services, and policy-led strategies constrained by ecological thresholds and institutional inertia. Compared with conventional static or equilibrium-based models, this approach provides a mathematically rigorous tool for examining delay-driven, nonlinear interactions in complex socio-ecological systems. The framework highlights the value of dynamical systems analysis for scenario exploration, policy design, and sustainable governance in resource-constrained environments.

1. Introduction

Port development supports global trade by enabling the circulation of goods, expanding regional market access, and mobilizing capital for infrastructure investment [1,2]. In developing economies, ports often become strategic growth drivers that stimulate industrial agglomeration and urban expansion under logistics-centered development policies [3]. As critical nodes of hydraulic infrastructure, ports not only regulate flows of goods but also influence coastal hydrological systems and land–water interfaces, thereby affecting regional water resource management and ecological stability [4,5]. When port, industrial, and city subsystems evolve without coordinated planning, mismatches emerge between transport capacity, production needs, and public service supply, ultimately constraining long-term development [6,7]. Addressing these mismatches requires planning strategies that integrate logistical functions with industrial transition goals and city system resilience targets [8].

The port–industry–city (PIC) framework offers an analytical basis upon which to examine such integration by capturing the interdependence among transportation infrastructure, productive sectors, and urban services [9,10,11]. Within this system, ports facilitate logistics operations, industries generate economic output, and cities provide labor, housing, and institutional support [12]. Their interactions form dynamic feedback loops whose efficiency shapes regional competitiveness, while poor coordination amplifies structural vulnerabilities [11]. For economies undergoing concurrent processes of industrial upgrading, urban infrastructure development, and trade expansion, coordinated PIC evolution is essential to achieving sustainability goals [9]. However, practical implementation is often challenged by overlapping regulatory jurisdictions, insufficient technical capacity, and volatile environmental or geopolitical conditions [13].

Mathematical modeling serves as a valuable tool to address these challenges, offering a structured framework for simulating the complex, dynamic interactions between port, industry, and city subsystems. By capturing nonlinear feedbacks and time delays, mathematical models can provide more accurate predictions, even in contexts where data are scarce and uncertainty is high. This capability is particularly advantageous in developing countries, where conventional models may fail to account for local complexities and data limitations. Through the application of such models, policymakers gain insights into system behaviors, improving decision-making processes and enhancing the efficiency of interventions. As demonstrated in previous studies, mathematical modeling can assist in predicting outcomes, optimizing system operations, and guiding long-term development strategies [14,15,16].

Existing studies have established fundamental theoretical frameworks and modeling paradigms for analyzing port–industry–city synergy mechanisms. Xu [17] developed a theoretical framework for port–maritime economic systems by innovatively integrating dynamic input–output models, game theory, and projection pursuit models, which formed the methodological foundation for subsequent research. Building upon this work, Zhang [18] constructed a multi-subsystem causal network from a system dynamics perspective, where entropy function analysis revealed the dissipative structure characteristics of port-city systems to support policy simulation. The advancement of complexity science has introduced co-evolution theory into this research domain [19], with threshold regression models demonstrating how ports, industries, and cities dynamically adapt to institutional changes and global shocks like COVID-19, while empirically validating the threshold effects of major events on system phase transitions. Furthermore, Zhao et al. [20] employed spatial econometric models to analyze the core–periphery spatial differentiation patterns in port clusters, systematically quantifying the positive spillover effects and heterogeneous spatial responses of port competitiveness on regional economic growth. Multi-agent system simulations have also been extensively applied to port facility planning decisions [21,22].

However, the extension of research to developing countries presents dual challenges for traditional modeling approaches due to data limitations and increasing system complexity. Conventional models typically require comprehensive continuous datasets, including port throughput [23] and industrial statistics [24], which are often unavailable for emerging ports like Kribi Deep Seaport in Cameroon. Moreover, these models frequently oversimplify real-world dynamics by assuming immediate returns on port investments, despite infrastructure projects commonly exhibiting multi-year time lags [25,26], while unexpected policy changes may trigger cascading uncertainties [27]. Current analytical tools that have been developed based on mature port experiences, such as that of Ningbo-Zhoushan Port [28,29], prove inadequate for regions with unique institutional environments and limited data monitoring capabilities. This situation urgently calls for innovative modeling approaches that can effectively address data deficiencies while accurately simulating time-lag effects and stochastic shocks, thereby providing policymakers with more flexible and adaptive decision-support platforms.

This study introduces an adaptive modeling framework designed for data-scarce environments by formalizing the dynamic co-evolution among port, industry, and city subsystems under uncertainty. The model captures endogenous time delays and nonlinear feedback using three key innovations. First, it applies a dimensionless indicator system that allows cross-regional generalization and parameter normalization. Second, it integrates delay-differential structures with stochastic components to represent both internal lag effects and exogenous shocks. Third, it embeds a response mechanism that models institutional inertia, capacity thresholds, and saturation constraints over time.

The proposed model contributes to both theoretical and applied research on infrastructure-led development. Theoretically, it extends the scope of co-evolution modeling by embedding delay-response mechanisms and random disturbances into PIC system dynamics, offering a more realistic depiction of system behavior under stress. Practically, the model generates development trajectory predictions under various policy scenarios through parameter adjustments, revealing evolutionary patterns of typical risk modes such as port overdevelopment and industrial transformation lags. The simulation mechanism offers decision support for port capacity optimization and regional risk warning systems, providing universally applicable references for port–city planning in developing countries.

The remainder of this paper is organized as follows. Section 2 outlines the structural features and interactions of the port–industry–city system. Section 3 develops a dynamic co-evolution model incorporating time delays and nonlinear feedbacks. Section 4 presents simulation results under different scenarios to analyze system behavior and policy impacts. Section 5 concludes with key findings and implications.

2. The Port–Industry–City System

2.1. Port Subsystem

The port subsystem is a key component of the integrated port–industry–city system, essential for regional logistics, infrastructure, and operations. It operates through two main dimensions: internal mechanisms and external linkages, as shown in Figure 1.

Internally, the subsystem is driven by two core factors: infrastructure level and operational capacity. The infrastructure level includes physical assets like terminals and storage facilities, which grow through reinvestment from operational revenue and logistics demand. However, depreciation presents a challenge, requiring continuous investment to maintain efficiency. Operational capacity reflects the quality of port management and service delivery, supported by financial resources and skilled labor, primarily provided by the city subsystem. Workforce attrition and institutional limitations can reduce operational efficiency. Together, infrastructure and operational capacity determine the port’s throughput and its revenue generation, which are reinvested to drive growth. A crucial aspect of the port subsystem is the measurement of the coastal resources, which tracks the efficiency of shoreline utilization relative to port infrastructure. This metric reflects how well the port leverages its geographical advantages, influencing overall capacity and growth potential.

Externally, the port subsystem relies on the support of the city and industry subsystems, along with broader environmental factors. The city subsystem contributes through transportation connectivity, labor supply, and administrative support. The industry subsystem, driven by logistics demand, fuels expansion in port facilities and services. Additionally, macro-level factors like competition from neighboring ports, national policies, and international financing availability shape the port’s development and strategic positioning.

2.2. Industry Subsystem

The industrial subsystem constitutes the production core of the port–industry–city system, acting as the primary source of logistics demand and a key driver of regional economic output. It typically develops around port-adjacent industrial zones, where sectors such as mineral processing, chemicals, and advanced manufacturing form integrated value chains from raw material intake to export. The dynamics of this subsystem can be understood through its internal mechanisms and external dependencies, as illustrated in Figure 2.

Internally, two core stock variables define the subsystem’s evolution: industrial structure and supply chain coordination. The industrial structure reflects the diversity and hierarchy of sectoral composition, shaped by changing market demands, technological upgrades, and industrial policies. Emerging industries expand with policy and investment support, while outdated sectors may decline due to obsolescence or market saturation, requiring continuous structural adjustment.

Supply chain coordination captures the degree of internal integration across procurement, production, and distribution. Higher coordination improves efficiency, product quality, and market responsiveness. This is facilitated by advanced logistics infrastructure and port services such as container handling and cold chain systems. However, disruptions in logistics or weak institutional links may reduce coordination effectiveness and system resilience.

The combined effects of structure and coordination determine industrial output, which directly shapes port throughput demand. As production capacity increases, the resulting logistics flow reinforces investment needs in both port and city subsystems, forming a self-reinforcing loop of industrial growth and infrastructure expansion.

Externally, the industrial subsystem depends on port services for reliable logistics and on the city subsystem for labor, transport connectivity, and administrative support. Skilled workforce availability, public investment, and favorable urban policies further enhance industrial performance and attract high-value-added industries. Additionally, international market demand plays a significant role in shaping industrial development by influencing export potential and global competitiveness. Changes in global market conditions, regional competition, and national industrial strategies impact long-term development and structural transformation.

2.3. City Subsystem

The city subsystem serves as a foundational support component within the integrated port–industry–city system, primarily by supplying labor, policy facilitation, and service functions to ensure the coordinated development of port and industrial activities. It shapes the system’s resilience through human capital provision, infrastructure development, and institutional capacity building. The system dynamics structure of the city subsystem is shown in Figure 3, which illustrates the interactions among industrialization, service capacity, population mobility, and their external linkages.

As shown in Figure 3, the internal dynamics of the city subsystem are driven by three key variables: the level of industrialization, the capacity of public services, and the scale of population inflow. The city’s industrialization reflects its ability to support production and logistics functions through manufacturing and processing sectors. This capacity increases through investment-driven industrial growth and declines through the relocation of outdated industries. Service capacity captures infrastructure such as transport, education, and healthcare, which underpins both resident welfare and economic operations. It is enhanced through public investment and is reduced by infrastructure aging. Population inflow reflects the city’s labor attractiveness and grows with employment opportunities and declines when costs rise or development slows.

These internal components jointly influence the efficiency and adaptability of the city subsystem, while also shaping the operational environment of the port and industry subsystems. As industrial and port development expand demand for services and labor, the city responds by upgrading infrastructure and absorbing labor inflows, reinforcing system-level integration.

Externally, the city subsystem interacts with the port subsystem by relying on logistics flows and employment provision, which stimulate consumption and support labor circulation. The industrial subsystem drives fiscal revenue and service demand, fostering urban growth. Broader external influences, such as national policies, capital inflows, and regional competition, further shape the city’s development path and its role within the integrated system.

3. The Model

Port–industry–city systems are complex adaptive structures involving deeply intertwined physical infrastructure, economic processes, and spatial transformations. Based on the preceding chapter’s analysis of subsystem functions and interconnections, this chapter advances a formalized modeling framework that distills the essential features of these systems into a tractable mathematical structure. Recognizing the high dimensionality and heterogeneity of real-world data, the model uses development level as the core conceptual variable to represent each subsystem, enabling the integration of port capacity, industrial output, and urban growth within a coherent dynamical system. The modeling strategy captures two core aspects of co-evolution: first, a time-delay dynamical model is constructed to reflect the physical and institutional lags inherent in infrastructure development, industrial upgrading, and policy feedbacks; second, an extended formulation introduces state-dependent interaction coefficients that evolve dynamically in response to system conditions, allowing for the representation of nonlinear effects such as diminishing returns, element mismatch, and threshold-triggered transitions. This abstraction retains the economic–physical logic of subsystem interactions while accommodating stochastic disturbances and endogenous feedback, thus providing a robust foundation for simulating co-development patterns, identifying coordination bottlenecks, and evaluating adaptive governance strategies in data-scarce environments.

3.1. Time-Delay Dynamical Model for Port–Industry–City Co-Evolution

The dynamic interactions of coordinated development among ports, industries, and cities are systematically characterized by time-delay differential equations (Equation (1)). The model parameters follow economic–physical mechanisms between elements. For mathematical rigor and to ensure bounded and meaningful dynamics, we additionally impose the condition that $P(t),I(t),C(t)\in \left[\mathrm{0,1}\right],\forall t>0$. In the port subsystem equation, $\alpha$ represents the marginal pulling effect of industrial scale on port cargo demand, with its denominator structure employing a saturation function to avoid theoretical deviations from infinite industrial expansion. $\beta$ acts as a dynamic regulation coefficient that implements negative feedback control by comparing real-time port throughput $P\left(t\right)$ with urban demand $\gamma C\left(t\right)$, thereby maintaining dynamic equilibrium between port scale and urban service capacity. $\mu$ embodies rigid physical constraints on port expansion, such as shoreline resources and channel depth.

The industry subsystem equation establishes a dual-drive mechanism. $\delta$ quantifies the enhancement effect of port efficiency on industrial competitiveness, while $\lambda$ measures the supporting role of urban public services in industrial upgrading. $\epsilon$ denotes the industrial decay rate caused by regional market competition and resource constraints, reflecting natural shrinkage of industrial scale. $\rho$ serves as a synergy coefficient capturing nonlinear gains from the coupling between port infrastructure and urban factor supply.

In the city subsystem equation, $\zeta$ reflects the employment creation effect from industrial agglomeration. $\eta$ characterizes the contribution of port trade radiation to urban economic scale. $\theta$ describes the inhibitory effect of resource–environmental constraints on urban expansion.

$$\left\{\begin{array}{c}{\displaystyle \frac{dP}{dt}}=\alpha {\displaystyle \frac{I\left(t-{\tau }_{IP}\right)}{1+\frac{I\left(t-{\tau }_{IP}\right)}{K_I}}}-\beta (P(t)-\gamma C(t))-\mu P(t)+{\sigma }_P{\xi }_P(t)\\ {\displaystyle \frac{dI}{dt}}=\delta {\displaystyle \frac{P\left(t-{\tau }_{PI}\right)}{1+\frac{P\left(t-{\tau }_{PI}\right)}{K_P}}}+\lambda {\displaystyle \frac{C\left(t-{\tau }_{CI}\right)}{1+\frac{C\left(t-{\tau }_{CI}\right)}{K_C}}}-\epsilon I\left(t\right)+\rho P\left(t-{\tau }_{PI}\right)C\left(t-{\tau }_{CI}\right)+{\sigma }_I{\xi }_I\left(t\right)\\ {\displaystyle \frac{dC}{dt}}=\zeta I\left(t\right)+\eta {\displaystyle \frac{P\left(t-{\tau }_{PC}\right)}{1+\frac{P\left(t-{\tau }_{PC}\right)}{K_P}}}-\theta C\left(t\right)+{\sigma }_C{\xi }_C\left(t\right)\end{array}\right..$$

(1)

The time-delay parameter system is designed based on the physical nature and economic transmission characteristics of inter-element interactions. The model incorporates four critical delays: ${\tau }_{IP}$ (industry → port), ${\tau }_{PI}$ (port → industry), ${\tau }_{CI}$ (city → industry), and ${\tau }_{PC}$ (port → city). ${\tau }_{IP}$ reflects the physical process cycle for converting industrial investments into port cargo demand, arising from time costs in industrial park construction, equipment installation, and production standardization. ${\tau }_{PI}$ corresponds to institutional delays in translating port efficiency improvements into industrial competitiveness, originating from organizational adaptations like supply chain restructuring. ${\tau }_{PC}$ describes the material evolution cycle of port expansion-driven urban spatial restructuring, covering processes such as port–road network construction and port–city integration zone development. ${\tau }_{CI}$ characterizes delayed supporting effects of urban public service investments on industrial upgrading, with its duration tied to knowledge conversion processes like human capital accumulation.

The exclusion of ${\tau }_{IC}$ (industry→city) and ${\tau }_{CP}$ (city→port) is theoretically justified. Industrial employment creation ($\zeta I\left(t\right)$) is an instantaneous economic behavior where production launch directly generates labor demand and consumer market expansion, transmitted through real-time price signals in labor and commodity markets. The regulatory effect of urban demand on port scale ($-\beta \left(P\left(t\right)-\gamma C\left(t\right)\right)$) reflects short-term market equilibrium mechanisms that require no physical spatial reconstruction. In contrast, port-to-city economic radiation ($\eta P\left(t-{\tau }_{PC}\right)$) necessitates retention of ${\tau }_{PC}$ as it depends on material evolution processes like industrial carrier construction and population migration.

Stochastic disturbances are injected into the system through three independent processes, ${\xi }_P\left(t\right)$, ${\xi }_I\left(t\right)$ and ${\xi }_C\left(t\right)$, with impact intensities controlled by ${\sigma }_P,{\sigma }_I$, and ${\sigma }_C$, respectively. These terms model exogenous uncertainties such as international trade fluctuations and geopolitical risks. Multilayer nonlinear mechanisms ensure physical rationality of system behavior. The denominator structure $1+X/K_X$ ($X\in \left\{I,P,C\right\}$) automatically triggers diminishing marginal returns when subsystem scales approach saturation thresholds $K_X$. The resistance term $\mu P(t)$ in the port equation grows with scale expansion, effectively preventing unrealistic infrastructure overdevelopment. The synergy term $\rho P\left(t-{\tau }_{PI}\right)C\left(t-{\tau }_{CI}\right)$ in the industry equation reveals non-linear growth patterns induced by element coupling, providing mathematical foundations for phase transition analysis. This modeling strategy theoretically accommodates multimodal scenarios including co-development, factor blockage, and external shocks.

3.2. State-Dependent Dynamic Interaction Extension Model

Building upon the endogenous nonlinear mechanisms revealed by the baseline model, time-varying parameters are introduced to capture the dynamic adaptability of developmental elements. The extended model expresses core interaction coefficients as system state-dependent functions, incorporating three mechanisms—proximity effects, diminishing marginal effects, and threshold response effects—to enable parameter responses to nonlinear feedback during system evolution. This enhances the model’s explanatory power for the complexity of port–industry–city co-development. The extended time-delay differential equations are as follows:

$$\left\{\begin{array}{c}{\displaystyle \frac{dP}{dt}}=\alpha (t){\displaystyle \frac{I\left(t-{\tau }_{IP}\right)}{1+\frac{I\left(t-{\tau }_{IP}\right)}{K_I}}}-\beta (t)(P(t)-\gamma C(t))-\mu (t)P(t)+{\sigma }_P{\xi }_P(t)\\ {\displaystyle \frac{dI}{dt}}=\delta \left(t\right){\displaystyle \frac{P\left(t-{\tau }_{PI}\right)}{1+\frac{P\left(t-{\tau }_{PI}\right)}{K_P}}}+\lambda {\displaystyle \frac{C\left(t-{\tau }_{CI}\right)}{1+\frac{C\left(t-{\tau }_{CI}\right)}{K_C}}}-\epsilon I\left(t\right)+\rho \left(t\right)P\left(t-{\tau }_{PI}\right)C\left(t-{\tau }_{CI}\right)+{\sigma }_I{\xi }_I\left(t\right)\\ {\displaystyle \frac{dC}{dt}}=\zeta I\left(t\right)+\eta \left(t\right){\displaystyle \frac{P\left(t-{\tau }_{PC}\right)}{1+\frac{P\left(t-{\tau }_{PC}\right)}{K_P}}}-\theta \left(t\right)C\left(t\right)+{\sigma }_C{\xi }_C\left(t\right)\end{array}\right..$$

(2)

The industrial pulling coefficient $\alpha \left(t\right)$ is constructed as an abstracted functional form based on empirical findings on the pulling effect of ports on industries [30,31]. It dynamically adjusts through coupled proximity and diminishing marginal effects, thereby reflecting synergistic efficiency in balanced element development, as follows:

$$\alpha \left(t\right)={\alpha }_0\cdot \exp \left(-k_{\alpha }\left|{\displaystyle \frac{I\left(t\right)}{P\left(t\right)}}-1\right|\right)\cdot {\displaystyle \frac{1}{1+{\left(\frac{P\left(t\right)}{K_P}\right)}^{n_{\alpha }}}}.$$

(3)

The exponential term expresses the well-documented mechanism of port–industry scale matching: synergy is maximized at balanced scales, and deviations reduce efficiency. The denominator represents diminishing marginal returns, consistent with economic evidence that the contribution of ports decreases as development approaches the saturation threshold $K_P$. Hence, Equation (3) should be viewed as an abstracted modeling framework distilled from empirical studies, rather than as a directly estimated equation.

The regulation coefficient $\beta \left(t\right)$ employs a threshold response mechanism, as follows:

$$\beta \left(t\right)={\beta }_0\cdot \left[1+\tanh \left({\lambda }_{\beta }\left({\displaystyle \frac{C\left(t\right)}{P\left(t\right)}}-{\varphi }_{\beta }\right)\right)\right].$$

(4)

When the port–city scale ratio $C/P$ exceeds critical value ${\varphi }_{\beta }$, the hyperbolic tangent function triggers strengthened negative feedback. Its smoothness avoids abrupt policy changes, accurately modeling reverse regulation (e.g., land supply controls) when urban services lag behind port expansion.

The port self-inhibition coefficient $\mu \left(t\right)$ characterizes nonlinear scale constraints, as follows:

$$\mu \left(t\right)={\mu }_0\cdot \left(1+{\left({\displaystyle \frac{P\left(t\right)}{K_P}}\right)}^m\right).$$

(5)

The power-law structure dominates inhibition as port scale approaches design capacity $K_P$, simulating nonlinear marginal cost escalation from shoreline scarcity.

The port promotion coefficient $\delta \left(t\right)$ achieves element balance via symmetric proximity effects, as follows:

$$\delta \left(t\right)={\delta }_0\cdot \exp \left(-k_{\delta }\left|{\displaystyle \frac{P\left(t\right)}{I\left(t\right)}}-1\right|\right).$$

(6)

Exponential decay weakens port-driven industrial pulling when $P/I$ deviates from equilibrium, quantifying resource idling risks from infrastructure–demand mismatches.

The synergy coefficient $\rho \left(t\right)$ implements gain enhancement, as follows:

$$\rho \left(t\right)={\rho }_0\cdot \left(1+{\displaystyle \frac{2}{1+\exp \left(-{\lambda }_{\rho }\left(P\left(t\right)C\left(t\right)-{\varphi }_{\rho }\right)\right)}}\right).$$

(7)

When $P\cdot C$ exceeds threshold ${\varphi }_{\rho }$, the sigmoid function triggers nonlinear synergy amplification, capturing multiplier effects from deep port–city integration. This reveals non-linear co-development momentum emerging after critical thresholds.

The port contribution coefficient $\eta \left(t\right)$ combines resource constraints and cyclical fluctuations, as follows:

$$\eta \left(t\right)={\eta }_0\cdot {\displaystyle \frac{1}{1+{\left(\frac{P\left(t\right)}{K_P}\right)}^{n_{\eta }}}}\cdot \left(1+{\nu }_{\eta }\sin \left({\displaystyle \frac{2\pi t}{T_{\eta }}}\right)\right).$$

(8)

The logistic term suppresses marginal returns from port overexpansion, while the sinusoidal term models policy cycle modulation.

The urban carrying capacity coefficient $\theta \left(t\right)$ employs threshold effects, as follows:

$$\theta \left(t\right)={\theta }_0\cdot \left(1+{\displaystyle \frac{1}{1+\exp \left(-{\lambda }_{\theta }\left(C\left(t\right)-{\varphi }_{\theta }{K}_C\right)\right)}}\right).$$

(9)

When urban development $C$ exceeds ${\varphi }_{\theta }{K}_C$, environmental constraints nonlinearly intensify, simulating accelerated inhibition from ecological degradation. Through coupled proximity, diminishing marginal, and threshold response effects, the model comprehensively captures element adaptability decay, scale saturation constraints, and critical state transitions in port–industry–city systems, establishing mathematical foundations for nonlinear evolutionary dynamics.

In constructing the dynamic parameter system, $\lambda$ (urban support coefficient) and $\zeta$ (industrial employment coefficient) remain static due to hierarchical abstraction principles in system dynamics and parameter economic implications. $\lambda$ represents the cumulative effects of infrastructure and institutional environments, which exhibit strong temporal inertia beyond the model’s simulation scale. Their delayed impacts are sufficiently captured by ${\tau }_{CI}$. $\zeta$ reflects job creation per industrial unit, constrained by slow variables like labor productivity during stable technological phases. Its dynamics are absorbed by the $\eta \left(t\right)P\left(t-{\tau }_{PC}\right)$ term. Core dynamic parameters ($\alpha \left(t\right),\beta \left(t\right), \delta \left(t\right)$, etc.) already cover primary nonlinear feedbacks. Excessive parameter dynamization would violate Occam’s razor, reducing model identifiability and policy interpretability. This selective dynamization balances mechanistic completeness with theoretical clarity.

3.3. Application Framework of the Port–Industry–City Co-Evolution Model

This section proposes an integrated application framework for the port–industry–city co-evolution model, systematically combining core mechanisms from the time-delay dynamical model and state-dependent interaction model. It establishes a complete pathway from theoretical modeling to empirical analysis. As shown in Figure 4, bidirectional mapping between theoretical models and real-world systems is constructed through multi-source data fusion and dynamic parameter adaptation mechanisms.

The framework comprises three hierarchical layers. The multi-source data input layer integrates three foundational data sources: an expert knowledge repository for subjective judgments, structured statistical databases, and unstructured environmental databases. The expert knowledge repository extracts qualitative insights (e.g., port planning, industrial policies) via the Delphi method, supporting prior parameter estimation and substitution calibration under data-deficient scenarios. Structured statistical databases consolidate time-series panel data (e.g., port throughput, industrial linkage indices) to objectively calibrate time-delay parameters and state-dependent weights. Unstructured environmental databases incorporate policy texts, geographic remote sensing images, and public sentiment data, which are converted into semi-structured parameters (e.g., policy shock intensity, ecological constraint thresholds) through NLP and image recognition technologies.

The dynamic model processing layer uses the time-delay dynamical equations and state-dependent interaction model as core algorithmic engines. It implements dual-path parameter optimization: time-delay parameters are calibrated via historical data fitting combined with expert knowledge weighting, while state-dependent weights are dynamically updated through Bayesian networks, achieving probabilistic fusion of subjective expertise and data-driven results.

The decision-making output layer generates three decision-support products: synergy degree indices, risk early-warning thresholds, and strategy prioritization. A feedback loop maps policy implementation effects to parameter updates in real time, forming an adaptive closed loop of “strategy intervention → effect evaluation → model iteration.”

The framework transcends traditional models’ reliance on linear assumptions and static parameters. While retaining functional cores of classical methods (e.g., input–output analysis, spatial econometrics), it corrects dynamic response deviations via time-delay operators and captures nonlinear interactions through state-dependent mechanisms. Its multi-level structure is designed to accommodate different spatial scales, including national strategic planning, regional port cluster coordination, and individual port operations. This design offers a scalable methodological toolkit suitable for studying port–industry–city systems in regions with limited data availability.

4. Simulation Analysis

4.1. Experiment Setting

Due to the scarcity of large-scale, consistent data in many developing regions—especially regarding emerging port systems—this study classifies three typical developmental archetypes of the port–industry–city system according to the dominant subsystem at the early stage: (1) port-led development driven by external capital, (2) industry-led development through endogenous clustering, and (3) city-led development under strong policy intervention. To ensure empirical relevance, we selected three real-world ports as representative cases for each type: the Kribi Deep Seaport in Cameroon, Ningbo-Zhoushan Port in China, and Singapore Port, respectively. The subsequent parameterization of initial conditions was conducted through a structured expert-informed approach to ensure cross-scenario comparability.

To determine the initial development ratios for ports, industries, and cities across the three modeled scenarios, we employed an expert-informed parameterization framework grounded in comparative regional data and structured consensus-building [32,33]. The process began with the compilation of a harmonized indicator system for each case region, aiming to reflect the relative maturity of the port (P), industry (I), and city (C) subsystems. Key indicators included GDP per capita, total population, industrial share of GDP, port throughput (in million tons or TEUs), and urbanization rate. These data served as empirical anchors for expert judgment.

Table 1. Summary of regional indicators for parameter estimation.

Data Dimension	Indicator
Economic capacity	GDP per capita (USD)
Urban scale	Total population (millions)
Industrial maturity	Industrial share of GDP (%)
Port development scale	Port throughput (million tons)
Urban development intensity	Urbanization rate (%)

summarizes the primary indicators used for anchoring expert estimates across the three port regions. Given the relative scarcity of data for Kribi, which is characteristic of many emerging infrastructure projects, we undertook efforts to align data dimensions across all case regions to ensure consistency.

Based on this aligned dataset, we conducted a structured elicitation exercise involving a panel of experts, including senior managers from the Kribi Port Authority, academic researchers in transport economics and regional planning, and government officials involved in infrastructure development. Experts were first presented with the regional data shown in Table 1 and then asked to estimate the relative initial development level of each subsystem (P, I, C) under each scenario, expressed as a proportion of that subsystem’s capacity limit.

To maintain consistency and interpretability, all expert estimates were constrained to discrete increments with a minimum unit of 0.05. This produced a limited set of possible values, including 0.1, 0.25, 0.5, 0.75, and 0.8, which facilitated comparison across experts and scenarios. The elicitation process followed an iterative consensus-reaching mechanism, in which expert inputs were aggregated anonymously and presented back to the group at each round. Experts could revise their estimates based on the observed group-level trends, allowing collective refinement of judgment. Consensus level (CL) was calculated to quantify the degree of agreement among experts, as follows:

$$CL=1-{\displaystyle \frac{1}{n}}\sqrt{\sum _{i=1}^n {\parallel {\mathit{x}}_{\mathit{i}}-\overline{\mathit{x}}\parallel }_2^2},$$

where $\overline{\mathit{x}}=\sum _{i=1}^n {\lambda }_i{\mathit{x}}_{\mathit{i}}=\sum _{i=1}^n {\displaystyle \frac{1}{n}}{\mathit{x}}_{\mathit{i}}.$ Consensus was achieved once the threshold $\alpha =0.75$ was reached. This procedure ensures that initial parameter values are plausible within the scenario-based framework and allows the model to explore the potential evolution of the port–industry–city system under different dominant-subsystem scenarios. The full schematic of this feedback and consensus mechanism is illustrated in Figure 5.

Following this process, we finalized the scenario-specific initial parameters for model simulation as shown in

Table 2. Scenario-specific initialization parameters and real-world references.

Development Mode	Initial Condition	Representative Port
Externally capital-driven	$P\left(0\right)=0.8K_P,$ $I\left(0\right)=0.1K_I,$ $C\left(0\right)=0.1K_C$	Kribi Deep Seaport (CMR)
Industrially endogenous-driven	$P\left(0\right)=0.25K_P,$ $I\left(0\right)=0.5K_I,$ $C\left(0\right)=0.25K_C$	Ningbo-Zhoushan Port (CHN)
Policy-dominated	$P\left(0\right)=0.25K_P,$ $I\left(0\right)=0.25K_I,$ $C\left(0\right)=0.5K_C$	Singapore Port (SGP)

. Each configuration captures one of the hypothesized development trajectories and reflects expert-validated real-world patterns.

This parameterization framework not only ensures that initial conditions are grounded in regional empirical realities, but also guarantees internal consistency and minimizes subjectivity through a structured expert process. It reflects both the complexity of real-world heterogeneity and the pragmatic need for data-aligned modeling in emerging contexts.

Building upon these scenario settings, we construct a multi-scenario simulation experiment system based on the port–industry–city co-evolution model, revealing dynamic differentiation patterns of the three development modes. These patterns are explored by assigning distinct combinations of initial conditions for P, I, and C, grounded in the theory of dynamical system stability domains [34], where differences in the system’s starting state lead to distinct steady-state outcomes.

A dual-dimensional evaluation index system is introduced to analyze long-term equilibrium characteristics and co-evolution quality. First, the overall development level index $\mathcal{L}$ is defined as the total scale of port–industry–city subsystems at the steady state, as follows:

$$\mathcal{L}=\underset{t\to \mathrm{\infty }}{lim}\left[P\left(t\right)+I\left(t\right)+C\left(t\right)\right].$$

(10)

This index measures the system’s comprehensive output capacity under resource constraints, with its theoretical maximum bounded by the sum of subsystem saturation thresholds ${(K}_P,K_I,K_C)$. Second, the co-development degree index $\mathcal{D}$ is established to reflect structural equilibrium via the maximum-minimum scale difference among subsystems, as follows:

$$\mathcal{D}=max\left(P\left(t\right),I\left(t\right),C\left(t\right)\right)-min\left(P\left(t\right),I\left(t\right),C\left(t\right)\right).$$

(11)

A smaller $\mathcal{D}$ indicates narrower development gaps among port, industry, and city, signifying a more synergistic equilibrium.

4.2. Trajectory Patterns of Port–Industry–City Development

This section analyzes the simulated evolution of port, industry, and city subsystems under the three development modes defined in Section 3.1. By assigning distinct initial conditions to reflect external capital dominance, industrial self-organization, and policy-driven priorities, we trace the dynamic growth trajectories and interaction patterns among subsystems over time. The results reveal mode-specific differences in development sequencing, subsystem coordination, and long-term structural balance. Each of the following subsections presents a detailed account of the trends observed in one development mode, along with sensitivity analysis to identify the key parameters shaping its outcomes.

4.2.1. Externally Capital-Driven Ports

Figure 6 illustrates the typical evolutionary trajectory of an externally capital-driven port system. In the initial development phase, the port development level (P) significantly leads, but due to lagging industry (I) and city (C) development, port functionality lacks effective support, causing its decline within the first decade before stabilizing into slow fluctuations. In contrast, the industrial development level rapidly rises after initial delays, surpassing port levels around the 10th year and maintaining steady growth, reflecting gradual enhancement of industrial adaptation to external capital. However, after the 35th year, industrial growth decelerates with intermittent fluctuations, indicating dual constraints from internal resource allocation and external demand. Urban development exhibits the most stable upward trend, starting with slow growth from system initiation and maintaining moderate increases between the 10th and 40th years, with minimal volatility, revealing lagged yet stable urban functional evolution. The evident temporal and dynamic mismatches among subsystems highlight structural contradictions in synergistic coupling under external capital-driven modes. The port’s early dominance fails to drive industrial agglomeration or urban service enhancement, instead encountering growth bottlenecks from delayed support systems, resulting in long-term functional misalignment and structural imbalance.

Table 3. Sensitivity analysis of key parameters in the port subsystem.

Port Subsystem	Parameter	P(∞) + I(∞) + C(∞)	$\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{a}\mathit{x}}-\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{i}\mathit{n}}$
Port–industry promotion coefficient	${\delta }_0=0.50$	1.0775	0.0735
	${\delta }_0=0.75$	1.7591	0.1363
	${\delta }_0=0.25$	0.8473	0.1407
Port–city economic spillover coefficient	${\eta }_0=0.50$	1.0775	0.0735
	${\eta }_0=0.75$	1.2620	0.1450
	${\eta }_0=0.25$	0.8633	0.1517

sensitivity analysis clarifies key evolutionary drivers. The port-to-industry promotion coefficient and port-to-city spillover coefficient critically shape system trajectories. Enhancing port-driven industrial effects significantly elevates overall development levels and narrows subsystem gaps, validating the pivotal role of cultivating port-proximate industrial clusters to resolve “strong port, weak industry” dilemmas. Conversely, port-to-city spillover exhibits nonlinear characteristics: moderate intensity boosts port–city synergy, but excessive spillover exacerbates internal imbalances, reflecting constraints from urban service lags on port efficiency.

For emerging port cities in developing nations, this study reveals two core pathways: First, establishing dynamic adaptation mechanisms between port economies and proximate industries by embedding localized industrial chains to convert port advantages into sustainable competitiveness. Second, coordinating port spillover with urban service upgrades to prevent resource outflows from urban delays. Without synergistic mechanisms, ports risk stagnation as primary resource hubs, trapping regions in “investment lock-in—revenue leakage” cycles. Policy design should prioritize optimizing port–hinterland industrial coupling and synchronizing urban service functions to enhance resource efficiency and regional value chain positioning.

4.2.2. Industrially Endogenous-Driven Ports

Figure 7 demonstrates the dynamic evolution processes of port, industry, and city subsystems under the industrially endogenous-driven mode. Overall trends reveal that the industrial development level initially experiences slight declines but quickly stabilizes and enters a recovery phase, maintaining systemic dominance between the 15th and 40th years, indicating strong industrial leadership in regional development. The port development level exhibits steady upward progression, gradually approaching industrial levels under industrial pulling effects, demonstrating its adaptive and responsive supporting role in this mode. Urban development also shows gradual growth but with greater volatility compared with ports and industries, particularly displaying post-30th-year declines that reflect mismatches between urban functional development and industrial expansion in later stages, exposing bottlenecks in temporal coordination and support capabilities. Collectively, this mode manifests an “industry-led, port-followed, urban-adjusted” pattern, yet internal coupling remains insufficient, particularly in phased misalignments of urban service functions in supporting industrial and port development.

Furthermore, despite strong endogenous industrial growth momentum, excessive expansion without timely port and urban responses strains logistics and public service systems, constraining overall synergistic efficiency. Therefore, the development of industrially endogenous-driven port cities hinges on establishing an effective ternary coupling mechanism to ensure dynamic adaptation and feedback loops among industrial expansion, port capacity enhancement, and urban functional improvement.

Parameter sensitivity analyses in Figure 8 and

Table 4. Sensitivity analysis of key parameters in the industry subsystem.

Industry Subsystem	Parameter	P(∞) + I(∞) + C(∞)	$\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{a}\mathit{x}}-\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{i}\mathit{n}}$
Industry–port pull efficiency	${\alpha }_0=0.20$	1.8802	0.4867
	${\alpha }_0=0.10$	1.4439	0.3494
	${\alpha }_0=0.30$	2.2250	0.5656
Industry–city employment contribution intensity	$\zeta =0.05$	1.8802	0.4867
	$\zeta =0.10$	2.2548	0.4185
	$\zeta =0.01$	1.6829	0.4878

elucidate regulatory mechanisms of the industry subsystem on co-evolution. Simulation results show that enhancing industry-to-port pulling efficiency significantly elevates overall system development levels and strengthens port functionality. However, widening gaps among subsystems indicate structural imbalances from overemphasizing industrial advantages, which suppress systemic synergy. Conversely, moderately improving the industry-to-city employment contribution intensity enhances urban responsiveness and fosters positive “industry-city” coupling, thereby boosting system stability and resilience. Excessive values, however, skew resource allocation toward city systems, inhibiting port functional transitions and creating internal consumption risks rather than synergistic progression.

Comprehensive experiments identify two systemic risks requiring vigilance in industrially endogenous-driven port cities. First, port capacity lags under industrial overexpansion elevate logistics bottlenecks and supply chain vulnerabilities. Second, industrial agglomeration outpacing urban service upgrades causes resource misallocation and efficiency losses. Further parameter combination analyses reveal that maintaining pulling efficiency and employment contribution within moderate ranges enables Pareto optimality—simultaneous scale expansion and structural coordination among the three subsystems.

For developing nations, constructing closed-loop feedback mechanisms among “industry-port-city” is critical. Extending industrial chains to enhance port hub connectivity and distribution efficiency must align with employment multiplier effects that activate comprehensive urban service upgrades. Neglecting dynamic adaptation and bidirectional transmission mechanisms traps regional competitiveness in “localized breakthroughs-systemic lags” path dependency. Policymakers should optimize synergistic transmission pathways from industrial advantages to port efficiency and urban functions, elevating resource allocation efficiency and regional value chain positioning.

4.2.3. Policy-Dominated Ports

Figure 9 demonstrates the development dynamics and interaction mechanisms among port, industry, and city subsystems under policy-dominated modes. The port subsystem exhibits a three-phase trajectory of “rapid rise, gradual growth, slight decline”: rapid initial growth (0–15 years) driven by infrastructure investments, mid-term deceleration (15–35 years) reflecting diminishing marginal effects, and post-35-year declines due to ecological constraints. The industry subsystem grows rapidly after initial adaptation but plateaus in later stages due to resource competition with port and city systems, showing marked fluctuations. Urban development displays a “three-phase fluctuation pattern”—initial decline (0–10 years) from a policy focus on ports limiting public services, a compensatory rebound (10–30 years) with policy rebalancing toward cities, and a post-30-year stabilization under intensified ecological constraints. This reflects temporal resource allocation complexities and systemic coupling challenges in policy-dominated modes.

Sensitivity analyses in

Table 5. Sensitivity analysis of key parameters in the city subsystem.

City Subsystem	Parameters	P(∞) + I(∞) + C(∞)	$\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{a}\mathit{x}}-\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{i}\mathit{n}}$
Urban carrying capacity	${\theta }_0=0.10$	2.0042	0.1481
	${\theta }_0=0.15$	0.9401	0.039
	${\theta }_0=0.05$	2.8734	0.1266
Policy stability	${\nu }_{\eta }=0.1$	2.0578	0.1157
	${\nu }_{\eta }=0.2$	2.0042	0.1481
	${\nu }_{\eta }=0.3$	1.9190	0.1806
	${\nu }_{\eta }=0.4$	1.8859	0.2110

reveal the city subsystem’s regulatory role. Reducing ecological constraints (lowering urban carrying capacity parameters) releases short-term growth potential but amplifies systemic imbalances, indicating ecological threshold relaxation risks long-term structural instability. Conversely, enhancing policy stability parameters improves subsystem scales and synergy, highlighting institutional coherence’s decisive role in sustainable co-evolution.

Policy-dominated port cities must coordinate two core relationships. First, dynamic adaptation between ecological constraints and development demands requires threshold controls to prevent overexploitation and ecosystem collapse. Second, synergy between policy stability and market flexibility ensures continuity and adaptability to enhance resource efficiency and systemic resilience. For developing nations, an “ecological constraint-policy stability dual-core driving mechanism” is critical. This involves setting port development ceilings based on regional carrying capacity through legislative tools while maintaining policy elasticity to respond to market dynamics, thereby balancing institutional rigidity and flexibility. This mechanism avoids “short-term expansion-long-term imbalance” traps, enabling multidimensional synergy among scale growth, structural coordination, and institutional resilience for high-quality transitions.

4.3. Comparative Assessment and Synergetic Evolution Strategy

Based on the evolutionary simulations and sensitivity results in Section 4.2, this section synthesizes a holistic comparison across the three development archetypes of port–industry–city (PIC) systems. These modes, namely port-led (Kribi, Cameroon), industry-led (Ningbo-Zhoushan, China), and city-led (Singapore), represent typical real-world pathways observed in both developing and developed port cities. Rather than evaluating subsystems in isolation, we focus on systemic performance along two dimensions: aggregate development level and coordination quality. Through this lens, we uncover the structural dynamics underlying each mode, identify their core bottlenecks, and extract an integrative co-evolution strategy that informs sustainable transitions in PIC systems.

The results highlight a central paradox: higher development scale (e.g., industry-led) often comes at the expense of subsystem imbalance, while structurally balanced systems (e.g., port-led) tend to suffer from limited scale. The city-led trajectory strikes a middle ground but remains vulnerable to ecological limits and temporal misalignments. These patterns affirm that sustainable PIC development cannot be anchored in a single dominant subsystem. Instead, achieving robust, resilient growth requires managing timing mismatches, feedback delays, and resource allocation tradeoffs across subsystems.

To make these tradeoffs explicit, we summarize performance outcomes across modes in

Table 6. Performance comparison across PIC development modes.

Development Mode	Representative Port	P(∞) + I(∞) + C(∞)	$\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{a}\mathit{x}}-\underset{\mathit{P},\mathit{I},\mathit{C}}{\mathit{m}\mathit{i}\mathit{n}}$
Port-led	Kribi Deep Seaport (CMR)	1.0775	0.0735
Industry-led	Ningbo-Zhoushan Port (CHN)	1.8802	0.4867
City-led	Singapore Port (SGP)	2.0042	0.1484

, and extract core mechanisms in

Table 7. Key mechanisms and constraints in each development mode.

Development Mode	Core Driver	Binding Constraint	Coordination Bottleneck	Key Regulatory Lever
Port-led	External capital	Weak industrial follow-up	Port lacks downstream functional support	Strengthen port–industry linkages
Industry-led	Endogenous clustering	Logistics and urban service lag	Urban services fail to match industry	Moderate industry-to-city pull
City-led	Stable policy regime	Ecological carrying limits	Temporal resource reallocation mismatch	Calibrate policy stability-flexibility

.

Across cases, a consistent pattern emerges, where a lack of mutual timing and response between subsystems impedes synergistic evolution. In the Kribi case, early port primacy without timely industrial anchoring leads to underutilized capacity. Ningbo’s industrial dynamism outpaces urban support, exposing it to infrastructure bottlenecks and systemic fragility. Singapore’s policy-driven balance maintains order early on but gradually faces ecological ceiling pressures due to compounding scale effects.

To address these tensions, a blended coordination strategy is essential—one that activates subsystem strengths in proper sequence and mediates their interactions over time. We propose an integrated framework of synergetic regulation, focusing on three strategic dimensions:

• Temporal coupling: Synchronize subsystem transitions (e.g., ports trigger industrial logistics, which in turn stimulate urban services).
• Feedback sensitivity: Embed responsive mechanisms to dynamically adjust policy, investment, and infrastructure in real time.
• Constraint calibration: Impose adaptive ecological and institutional thresholds to prevent irreversible overshoot.

This comparative analysis suggests that successful port cities must evolve from single-core dominance to multi-core co-regulation. That is, from being “port-first” or “industry-first,” they must become coordinated systems that recognize lag structures, feedback asymmetries, and ecological interdependence. For policymakers in developing countries, this implies the need to design governance systems that balance strategic patience with dynamic responsiveness. Ports should be developed not merely as gateways, but as integrated nodes within adaptable industrial and urban networks.

4.4. Impact of Case-Region Heterogeneity on PIC System Evolution

In order to understand the impact of regional heterogeneity on the evolution of port–industry–city (PIC) systems, it is crucial to build an analytical framework linking regional characteristics, model parameters, and evolutionary paths. This subsection contrasts the differences in capital access channels, industrial bases, and policy environments across the case regions of Kribi (Cameroon), Ningbo-Zhoushan (China), and Singapore, to explore how these differences influence key model parameters and lead to divergent evolutionary trajectories.

(a)

Capital Access Channels and Investment Efficiency

The capital access channels in each region play a critical role in shaping the investment efficiency and overall development trajectory of the PIC system. In Cameroon (Kribi), capital access is primarily external, relying on international funding and investments. This external dependency limits the speed of industrial expansion and results in low investment efficiency (e.g., lower industrial decay rate ε) and slower infrastructure development. On the other hand, China (Ningbo-Zhoushan) benefits from both external and endogenous capital, with local industries driving much of the investment. This enables higher investment efficiency but also creates challenges in terms of urban services lagging behind industrial growth. Lastly, Singapore operates with a highly stable policy-driven capital access, where state-led investments ensure both high investment efficiency and long-term stability. The high level of policy stability in Singapore enables greater control over system evolution, particularly in terms of ensuring smooth coordination across subsystems.

(b)

Industrial Base and Structural Transition

The industrial base of each region significantly impacts the industrial decay rate (ε) and the evolution of the subsystem. Kribi, with its more limited industrial base, experiences a slower pace of industrial development, which contributes to lower industrial output and delayed port throughput demand. This slow growth makes it more vulnerable to a lack of synergy between subsystems. In contrast, Ningbo-Zhoushan has a well-established industrial base that grows rapidly, leading to a higher industrial decay rate as old industries face market saturation. This rapid industrial expansion outpaces the urban services sector, creating a mismatch between industrial growth and urban support, which hinders effective coordination. Singapore, with its advanced manufacturing and service-oriented economy, faces minimal industrial decay, as its industries evolve with strong institutional support, allowing for a smooth transition between industrial phases.

(c)

Policy and Institutional Impact on System Synergy

The policy and institutional environment plays a crucial role in shaping the dynamic evolution of the PIC system. Singapore’s policy-led mode stands out for its high policy stability, which enables effective coordination across subsystems. The government’s proactive role in regulating the economy and providing long-term investments enhances system-level synergy. In this policy-driven model, the policy stability parameter acts as a key enabler, promoting sustainable growth and mitigating potential disruptions caused by environmental or industrial shifts. This policy advantage contrasts with Cameroon, where weaker institutional frameworks and policy instability hinder long-term system cohesion, and China, where policy-driven investments are sometimes overwhelmed by the pace of industrial growth, leading to inefficiencies.

The differences in capital access, industrial base, and policy stability between the case regions explain the divergent evolutionary paths observed in the PIC system. In regions like Kribi, external capital reliance and limited industrial capacity slow down system evolution, leading to underutilization of infrastructure. In Ningbo-Zhoushan, rapid industrial growth and capital availability outpace urban development, resulting in a lack of balance and sustainability. Singapore, with its strong policy framework, manages to achieve a balanced and synergistic evolution, but faces challenges from ecological limits and resource allocation mismatches over time.

5. Conclusions

This study constructs a novel port–industry–city co-evolution model, providing an innovative analytical tool for exploring port–economic system dynamics in data-scarce regions. Research demonstrates that the dynamic evolution of port–industry–city systems is constrained not only by real-time interactions among elements but also by long-term and stochastic factors such as infrastructure investment return cycles, policy transmission delays, and international trade fluctuations. The model introduces dynamic parameter modulation mechanisms to effectively characterize nonlinear developmental features, revealing the evolutionary paths of three typical development modes: externally capital-driven modes, which require vigilance against resource misallocation from premature port construction; industrially endogenous-driven development, which demands temporal coordination between industrial agglomeration and urban service upgrades; and policy-dominated pathways, which necessitate dynamic adaptation mechanisms balancing ecological constraints and development demands to ensure sustainability.

Comparative assessment of representative ports—Kribi Deep Seaport (Cameroon), Ningbo-Zhoushan Port (China), and Singapore Port—demonstrates that different development modes yield distinct trade-offs between growth scale and subsystem coordination. City-led strategies achieve the highest overall development levels with moderate coordination efficiency. Industry-led models exhibit intermediate performance but suffer from the greatest structural imbalance. Port-led pathways offer the most balanced but comparatively slower growth. These patterns underscore the importance of timing and alignment across subsystems, with key coordination bottlenecks and regulatory levers varying by mode. The synthesis mechanism framework proposed in this study highlights the necessity of embedding adaptive feedback loops, stabilizing policy interfaces, and controlling ecological thresholds to promote synergistic evolution.

Compared with traditional methods, this study’s core innovation lies in establishing a transferable theoretical framework for analyzing the co-evolution of port–industry–city systems. Data-wise, dimensionless indicator construction and logical mapping mechanisms help address the challenge of incomplete or inconsistent data, which is often a limitation in emerging port economies. Mechanism-wise, incorporating time-delay effects and stochastic disturbances provides a more nuanced understanding of the long-term dynamics and feedback loops within the system. Application-wise, the model offers a flexible platform for testing various policy scenarios, allowing for a better understanding of potential pathways for port, industry, and city development.

However, there are several limitations to consider. Model applicability is inherently constrained by the assumptions made to generalize across regions with different institutional contexts and economic conditions. While the model is designed to be adaptable, it may not fully account for the unique governance structures and local political economies that influence development outcomes. Future studies could focus on refining the model’s regional specificity by incorporating local regulatory and institutional variables to improve its relevance to diverse contexts.

Variable specification remains another challenge. Although the model captures key dynamics of the port–industry–city system, the simplification of certain variables, such as ecological and social factors, might limit its ability to fully capture complex, real-world dynamics in some regions. Future improvements could focus on incorporating additional variables that better reflect these dynamics, such as social resilience or environmental thresholds, which could offer deeper insights into sustainable development pathways.

Finally, data acquisition continues to be a limitation in data-scarce regions, where comprehensive and continuous datasets are often unavailable. While the model is designed to function in such contexts, the lack of reliable data still impacts the precision of some inputs. Future research could explore the integration of alternative data sources, such as satellite imagery or micro-level economic data, to improve the model’s calibration and adaptability.

Overall, this study’s model provides valuable insights for policymakers by highlighting key interactions and feedback loops within port–industry–city systems. Future work should refine the model by incorporating region-specific data, expanding the set of variables considered, and improving data acquisition methods. These improvements will enhance the model’s capacity to support evidence-based decision-making for sustainable port development in emerging economies.