The Influence of Innovative Resources on the Comprehensive Carrying Capacity of China’s Urban Agglomerations: A System Dynamics Perspective

Abstract

The sustainable development of urban agglomerations greatly relies on their comprehensive carrying capacity (CCC). As society evolves, innovative resources emerge as core assets and serve as crucial pillars of this capacity. Despite existing CCC studies, the influence of innovative resources remains underexplored. This study analyzes the influence of innovative resources on the CCC of 19 urban agglomerations in China using a system dynamics approach. We find that innovative resources are an important subsystem of CCC. Increasing innovative resources is an effective strategy for enhancing CCC, yet the effects of different types of innovative resources vary. Merely increasing the number of universities and research institutions does not significantly improve the CCC level. Increasing the expenditures of higher education institutions, internal R&D, and the number of patents are effective approaches to enhance CCC. Moreover, these factors can form a virtuous cycle, mutually promoting innovation and CCC development, thus injecting new momentum into the sustainable development of urban agglomerations.

1. Introduction

Owing to the pandemic-induced economic downturn, cities worldwide have been influenced by multiple unexpected domestic and international factors [1]. Future success in building a modern socialist powerhouse requires sustainable urban development [2]. According to statistical data, the world’s urbanization rate reached 60% in 2022, and by 2050, two-thirds of the world’s population is predicted to live in cities [3]. The most common spatial organization in urban areas is urban agglomeration [4], relatively complete urban complexes centered around one or two core cities within a specific region and connected through an integrated transportation network.

Urban agglomerations are the products of urban interactions and carriers for efficient economic system operations [5]. They facilitate the free flow of factors, the large-scale aggregation of resources, geographical division of labor, a reduction in transaction costs for enterprises, and optimization of industrial chains. Urban agglomerations are the lifeblood and new growth poles of urban economic development and the basic units for participating in global competition [6]. For instance, urban agglomerations—such as the West Midlands and Central Scotland in the UK, the Ruhr region in Germany, and the Beijing-Tianjin-Hebei region in China have achieved significant economies of scale [7,8].

Despite their vast potential, urban agglomerations face significant sustainability challenges. With the large-scale influx of people and the rapid expansion of urban scale, the contradiction between the demand for a quality living environment and the relative inadequacy of urban agglomeration development is becoming increasingly apparent. Issues such as the environment [9], transportation [10], ecological quality [11], employment [12], housing [13], and public security have severely hindered the sustainable development of urban agglomerations.

The goal of sustainable development in urban agglomerations is to address multifaceted challenges in the social, economic, and environmental domains [14]. Central to this endeavor is the maximization of the CCC of urban agglomerations, encompassing diverse subsystems. These subsystems include resource-carrying capacity, ecological and environmental resilience, urban infrastructural sustainability, and various social resource capacities. The interplay of various factors, the coordinated growth of cohesive subgroups within agglomerations, and the functional optimization and upgrading of individual cities within these clusters jointly influence these subsystems. Consequently, they form resilient and dynamically adaptive systems that can withstand and respond to changing challenges.

Innovative resources play an important role in CCC. A lack of innovative resources lowers productivity, results in outdated environmental protection technologies, and increases pollution and waste. Nokia, once a giant in mobile phone manufacturing, peaked in the late 20th and early 21st centuries. Its core competitiveness lay in hardware manufacturing; however, with the rise of smartphones and the mobile internet, the market’s demand for software and ecosystems has increased daily. Nokia’s insufficient investment and innovation in software and application development meant that it failed to adapt to market changes over time, ultimately causing its decline [15].

Urban agglomerations have extremely significant innovative characteristics, and innovative resources play a pivotal role in enhancing their CCC [16,17]. With distinct innovative attributes, China’s urban agglomerations have gathered numerous scientific research institutions, higher learning institutions, and high-end talents to form a unique innovative ecosystem. Therefore, studying the influence of innovative resources on the CCC of China’s urban agglomerations is crucial for gaining a deeper understanding of their carrying capacity status, optimizing innovative resources, and enhancing their overall competitiveness. Through scientific planning and innovation-driven development, countries can better leverage innovative advantages, promote industrial structure upgrading and comprehensive economic and social development, and achieve high-quality and sustainable development of urban agglomerations in the future.

The remaining content of this article is as follows: the first part is a literature review; the second part is the research basis; the third part is the research framework; the fourth part is an analysis of the results; the fifth part is the conclusions and policy implications; the sixth part comprises the appendices, including Appendix A, Appendix B, Appendix C, Appendix D and Appendix E on the values of CCC and its subsystems and Appendix F on the abbreviations in this paper and their corresponding full forms.

2. Literature Review

2.1. Research on Innovative Resources

Romer’s theory [18] on the role of knowledge in economic growth profoundly reveals the positive influence of knowledge and skills on the economy, establishing a theoretical foundation for studying innovative resources. Subsequently, researchers have established a close link between knowledge-intensive services, innovation, and the effective utilization of innovative resources, emphasizing mutual reinforcement among the three [19]. Moreover, the significant influence of knowledge spillovers on the formation of industrial structures has been widely discussed, with foreign direct investment and industrial clustering recognized as key factors in enhancing the effectiveness of urban innovative resources [20]. Additionally, some scholars have considered innovative resources the core element in analyzing the role of internal spatial integration and coordinated industrial development in the urban agglomerations of the Yangtze River Economic Belt [21]. Furthermore, research has revealed that the rapid convergence of innovation within urban agglomerations is significantly influenced by the spillover of human capital and market interactions, both of which jointly enhance the utilization efficiency of innovative resources [22]. Finally, studies have indicated that the positive spillover effects of regional innovative capital surpass those of innovative talents, highlighting the dominant role of capital resources in driving innovation [23]. In summary, these studies underscore the crucial role of innovative resources in promoting innovation and sustainable urban development and reveal their active roles through aggregation and spillover effects.

2.2. Research on CCC

In 1943, carrying capacity was defined as the maximum density of a population that could be sustained by a given amount of biomass [24]. With rapid economic development in the 1970s, the global population soared, precipitating a continuous decline in per capita arable land. Consequently, the conflict between human activities and the ecological environment has become increasingly prominent. This has prompted scholars to focus on single-element carrying capacities, such as population [25], water [26,27], land, traffic [28], and resources [29,30].

In the 21st century, economic development and industrial structure upgrades have shifted attention beyond mere resources and the environment to encompass a broader range of carrying objects. Concepts such as economic and social carrying capacities have also been proposed. Furthermore, the accelerated urbanization process has comprehensively impacted the carrying capacity of modern urban agglomerations, prompting the emergence of the concept of CCC [31]. Despite the lack of a unified definition among the academic community, studying urban carrying capacity from the perspective of multiple factors—including land and water resources, the environment, ecosystems, urban infrastructure, social resources, economy, population, and transportation—has become a new trend. For instance, some scholars argue that urban CCC should incorporate not only natural environmental and resource factors but also urban energy and ecological factors [32]. To evaluate the CCC of China’s Yangtze River Economic Belt, factors such as ecological environment carrying capacity, transportation carrying capacity, factor market carrying capacity, and industrial economy carrying capacity were included in the evaluation framework [33].

Based on the literature review, we condense the CCC framework into three interdependent subsystems that collectively define a region’s sustainability threshold: economic carrying capacity (ECC), which encapsulates the ability of an economy to sustainably grow while ensuring economic stability, job creation, and the equitable distribution of wealth; public service carrying capacity (PSCC), reflecting the capacity of infrastructure and services, such as healthcare, education, transportation, and governance, to meet the demands of the population without compromising quality or accessibility; and natural resource carrying capacity (NRCC), which assesses the sustainability of a region’s natural resources, including water, land, air, and biodiversity, to support human activities without depletion or irreversible degradation. These three subsystems interplay, reinforcing or constraining each other, ultimately determining the overall CCC of a given region.

2.3. Research on the Influence of Innovative Resources on CCC

The existing literature primarily explores the spatial spillover and regional convergence effects of innovation activities, such as the promotion of economic growth, environmental optimization, and efficiency enhancement [34,35,36]. This finding indirectly validates the beneficial influence of allocating innovative resources on CCC development in urban agglomerations. Additionally, innovative resources exhibit real-time mobility both internally and across urban agglomerations and are utilized in diverse fields, including pollution control [37], transportation [38], communication [39], infrastructure [40], and enterprise production lines [41]. Despite these advancements, scholars have not explored the specific influence of innovative resources on CCC.

Thus, inspired by this gap in the existing research and building upon the foundational frameworks of ECC, PSCC, and NRCC, we propose the inclusion of innovative resource carrying capacity (IRCC) as a fourth, equally essential subsystem within the CCC paradigm. By incorporating IRCC, we aim to explore the specific mechanisms through which innovative resources contribute to CCC development, examining their influence on fostering economic growth with reduced environmental footprints, enhancing public services through technological advancements, and safeguarding natural resources through smart and sustainable utilization practices. Ultimately, this research endeavor seeks to provide a holistic understanding of how the optimization of innovative resources can serve as a strategic tool for advancing the sustainability threshold of urban agglomerations worldwide.

This study is expected to make the following academic contributions: First, we optimize the existing evaluation methods for the CCC index system, and this optimization process particularly focuses on innovative resources and treats them—along with economic, social, and natural resources—as subsystems of CCC. Second, to analyze the influence of changes in innovative resources on the future CCC of urban agglomerations better, we construct a system dynamics model. Finally, this study’s conclusions have rich policy implications, guiding future urban planning and development decisions to achieve more sustainable and efficient urban agglomeration development.

3. Research Basis

3.1. Theoretical Basis of CCC

The intricate interplay and multifaceted influences of NRCC, PSCC, ECC, and IRCC form the cornerstone of CCC in urban agglomerations. Each of these subsystems exerts a profound and interdependent effect on the overall sustainability and resilience of a region, constituting a complex yet harmonious web of factors that drive development. The subsequent paragraphs will explore the specifics of the specific roles and contributions of these individual components, elucidating how natural resources, vital public services, economic dynamics, and innovative resources intertwine to shape and enhance the CCC of urban agglomerations.

Natural resources, such as land, water and environment, constitute the material foundation for urban and social development, and their quantity, quality, and distribution have a direct influence on the CCC of a region [42]. For instance, scarcity of water resources can constrain the development of agriculture and industry, subsequently affecting the overall economic operation.

Vital public services, including healthcare, transportation, parks, and public budgets, improve urban life, strengthen a city’s attractiveness, and ultimately boost its CCC [43].

ECC reflects the economic scale and growth rate. A a region can sustain within a specific period, directly impacting employment, income, and fiscal conditions, providing solid material support for CCC [44].

Innovative resources, encompassing technological talent, research and development funds, and an innovative environment, are core elements driving social and economic progress [45]. Increasing IRCC enhances a region’s innovation and competitiveness, continuously boosting CCC.

In conclusion, NRCC, PSCC, ECC, and IRCC work together to shape a region’s CCC, relying on and enhancing each other. This intricate interplay seeks sustainable development within a dynamic balance.

3.2. System Dynamics Methodology

This study employs a system dynamics model to simulate the development trends in innovative resource and CCC in China’s urban agglomerations. System dynamics, founded by Forrester [46], combines system science with computer simulation, focusing on studying the feedback structure and behavior of systems. When dealing with complex systems, it decomposes the system, quantifies the interactive relationships, and simulates system operations, providing guidance for the design of real-world systems.

The advantage of system dynamics modeling lies in its ability to handle complex system problems. First, it is able to accurately quantify the interactive relationships between the system elements. Second, it can comprehensively consider numerous indicators and the utilization of historical data, enhancing the accuracy of its predictions and decision-making. Third, it has powerful data analysis capabilities, supporting multi-dimensional analysis and providing strong support for optimizing resource allocation and enhancing comprehensive carrying capacity. And finally, its approach of treating system movement as fluid motion enables rapid identification and description of complex systems, thus ensuring the efficiency and accuracy of research [47].

4. Research Framework

4.1. Research Scope and Data Sources

The 14th Five-Year Plan [48] proposes 19 urban agglomerations for optimization, growth, and cultivation, and the relevant departments have approved the corresponding core cities for the urban agglomerations. This has played an important role in the development of China’s urban agglomerations. Based on this, 31 core cities from 5 national-level, 8 regional-level, and 6 regional-level urban agglomerations were selected as samples (Figure 1). However, because of a lack of significant data, Hong Kong, the core city of the Pearl River Delta urban agglomeration, was not included. In addition, this research covers a time span from 2011 to 2040, with 2011–2020 representing historical data and 2021–2040 being predicted data.

4.2. Selection of the Indicators and Calculation Method for Historical CCC Values

The determination of the indicator boundaries is the foundation for evaluating the CCC of urban agglomerations. Owing to the numerous elements and complex relationships in the urban agglomeration system, the selection of indicators should follow the following principles to accurately express multidimensional variables: completeness, comprehensive coverage of all the aspects of the urban agglomeration, and the avoidance of research limitations; relevance, selecting representative and accurate indicators to reflect the evaluation goals and weaknesses; universality, selecting indicators that share common characteristics across all urban agglomerations; and operability, selecting data that are easy to obtain, organize, quantify, and operate to ensure data authenticity and subsequent research feasibility [49].

This study explores the influence of innovative resources on the CCC of urban agglomerations. Innovative resources refer to resources that introduce unprecedented new combinations of production factors and conditions into the production system, which can improve production efficiency and the ecological environment, showcase innovative achievements, and increase marginal returns [50]. Based on the definition of innovative resources and the principles of the indicator selection, the innovative resource-carrying capacity (IRCC) of urban agglomerations primarily encompasses research institutions, talents, funds, and innovative accomplishments. In terms of talent resources, we adopted the following four indicators: the number of college teachers; the number of jobs in scientific research and technology services; the number of jobs in information transmission, software, and information technology services; and R&D employment. In terms of financial resources, we focused on two key indicators, namely higher education funding and internal R&D expenditure. However, the regression analysis revealed that the expenditure of higher education institutions is primarily influenced by the education public budget expenditure and serves as a key determinant of the number of college teachers. To avoid redundant variable calculations, we did not consider higher education funding as an independent indicator when assessing the IRCC. Finally, we adopted the innovation achievement indicator of patent application authorization to measure the innovation capability of the urban agglomerations. In summary, the level of IRCC in urban agglomerations in this study was obtained from the weighted sum of seven innovative resource indicators, including the number of ordinary higher education and research institutes mentioned above.

According to the selection principle for the indicators and the research of scholars [51,52,53], we referred to national and provincial policy norms, as well as industry standards, to construct a CCC evaluation system for urban agglomerations, which includes the four subsystems of IRCC, economic carrying capacity (ECC), public service carrying capacity (PSCC), and natural resource carrying capacity (NRCC). Based on the requirements of system dynamics modeling and data availability, 28 indicators were selected for these four subsystems. Historical data were obtained from the National Bureau of Statistics, the statistical yearbooks of various cities, the China Economic Database, and the EPS Database (

Table 1. Multi indicator evaluation system and its weights for the CCC of urban agglomerations.

Criterion Layer	Criteria Weights	Indicator Layer	Indicator Weight	Basis for Selection
Innovative resource carrying capacity (IRCC)	0.2464	Number of ordinary higher education institutions and research institutes	0.0493	Research on innovative resources from the perspective of enterprises [54] and city [55]
		College teachers	0.0376
		Employment in scientific research and technology services	0.0320
		Employment in information transmission, software, and information technology services	0.0312
		R&D employment numbers	0.0381
		Internal R&D expenditure	0.0306
		Patent application authorization volume	0.0276
Economic carrying capacity (ECC)	0.3482	Per capita GDP	0.0331	Indicators of ECC and the impact of economic development on CCC [56,57]
		Proportion of the added value of the secondary industry in GDP	0.0383
		Proportion of the added value of the tertiary industry in GDP	0.0365
		Proportion of employment in the tertiary industry	0.0314
		Disposable income of urban residents	0.0397
		Completed housing area of real estate development enterprises	0.036
		Total profit	0.0348
		Savings deposit balance	0.0381
		Total sales of wholesale and retail goods above quota	0.0277
		Average salary of urban on-the-job employees	0.0326
Public service carrying capacity (PSCC)	0.2398	Road area	0.0416	Evaluation method for urban PSCC [58,59]
		Park green space- area	0.049
		Total collection of books in public libraries	0.0448
		Number of healthcare personnel in hospitals and health centers	0.0304
		Education public budget expenditure	0.0402
		Public budget expenditures for science and technology	0.0338
Natural resource carrying capacity (NRCC)	0.1769	Built-up area	0.0456	Comprehensive evaluation of resource and environmental carrying capacity [60,61]
		Harmless treatment rate of household waste	0.0409
		Centralized treatment rate of sewage treatment plants	0.0267
		Industrial sulfur dioxide emissions	0.0294
		Industrial smoke and dust emissions	0.0343

).

The variables involved in the CCC have different definitions and orders of magnitude; therefore, dimensional consistency processing is required before starting to work with the model. The comparison indicates that most variables positively influence CCC, with only industrial sulfur dioxide emissions and industrial smoke and dust emissions exerting a negative influence. The higher the value of the positive influencing variable, the higher the CCC, while the opposite is true for negative influencing variables. To ensure consistency in the direction of influence of the processed data on the load-bearing structure, this study adopted different methods of dimensional consistency treatment for the positive and negative influencing variables. The positively influencing variables were processed using Equation (1), whereas the negatively influencing variables were processed using Equation (2).

$${\alpha }_{ij}={\displaystyle \frac{{\beta }_{ij}-{\beta }_{\min }}{{\beta }_{\max }-{\beta }_{\min }}}(i=1,2,\cdots n;j=1,2,\cdots m)$$

(1)

$${\alpha }_{ij}={\displaystyle \frac{{\beta }_{\max }-{\beta }_{ij}}{{\beta }_{\max }-{\beta }_{\min }}}(i=1,2,\cdots n;j=1,2,\cdots m)$$

(2)

where $i$ is the region serial number; $j$ is the annual serial number; ${\alpha }_{ij}$ stands for the variables after consistency processing; ${\beta }_{ij}$ stands for the raw data; and ${\beta }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\beta }_{\mathrm{m}\mathrm{i}\mathrm{n}}$ are the maximum and minimum values in all the raw data corresponding to a single variable, respectively.

Weighting methods for CCC indicators can be divided into subjective and objective weighting methods. The CCC system is complex, and subjective calculations are prone to bias; therefore, selecting a suitable objective weighting method is necessary. Among them, the principal component analysis method highly depends on the main indicators, resulting in an excessive weight of the main indicators. Thus, some factors affecting CCC cannot be reflected. The entropy rule is sensitive to abnormal data, and statistical errors in individual data can interfere with the simulation results. The mean square error method can fully consider the differences and influences between various indicators, accurately compare the differences between regions and the same region at different time points, improve the accuracy and comprehensiveness of the CCC evaluation, and is a more suitable objective weighting method for this study. The calculation step for this method first involves measuring the internal differences of variables in different regions and years and then calculating the CCC by weighting the contribution rate of variances. The specific calculation process is elucidated in Equations (3)–(6).

Step 1:

$$A_k={\displaystyle \frac{1}{l}}{\displaystyle \sum {\alpha }_{ij}}(k=1,2,\cdots q;i=1,2,\cdots n;j=1,2,\cdots m)$$

(3)

where $A_k$ stands for the relevant indicators of the CCC and $l$ is the total amount of data covered by each indicator.

Step 2: Calculate the mean square deviation of each indicator $D_k$; see Equation (4).

$$D_k=\sqrt{{\displaystyle \frac{1}{l}}{\displaystyle \sum ({\alpha }_{ij}}-A_k{)}^2}(k=1,2,\cdots q;i=1,2,\cdots n;j=1,2,\cdots m)$$

(4)

Step 3: Calculate the weights of each indicator $W_k$; see Equation (5).

$$W_k={\displaystyle \frac{D_k}{{\displaystyle {\sum }_{k=1}^q{D}_k}}}$$

(5)

Step 4: Calculate the CCC; see Equation (6).

$$\mathrm{CCC}={\displaystyle \sum W_k}{\alpha }_{ij}(k=1,2,\cdots q;i=1,2,\cdots n;j=1,2,\cdots m)$$

(6)

Based on this study’s actual situation, the CCC includes 31 sample cities and 28 evaluation variables over 10 years. Therefore, in Equations (1)–(6), $n$ stands for 31, $m$ stands for 10, $q$ stands for 28, and $l$ stands for 310.

By combining the indicator system and Equations (1)–(6) selected herein, the weights of each criterion and the indicator layers were calculated (Table 1). The weight of each indicator layer for IRCC was approximately 0.03, with the highest weight being the number of ordinary higher education institutions and research institutes (0.0493) and the lowest being the number of patent applications and authorizations (0.0276), with minimal difference in the weight values. This indicates that although a certain degree of imbalance exists in the allocation of innovative resources among cities within Chinese urban agglomerations, different types of innovative resources can still maintain a certain degree of balance overall.

The calculation methods for IRCC, ECC, PSCC, and NRCC are similar to CCC, and they are all derived from the containing indicators. As can be seen in Table 1, four subsystems comprise seven, one, six, and five indicators, respectively, and their values are calculated based on the metrics within each subsystem. The values of IRCC, ECC, PSCC, NRCC, and CCC for the cities included in this study from 2011 to 2020 are detailed in Appendix A, Appendix B, Appendix C, Appendix D and Appendix E.

4.3. The Simulation Prediction Framework for IRCC and CCC Based on System Dynamics

Current approaches to carrying capacity modeling include synthetic control [62], neural networks [63], and system dynamics [64,65,66]. Synthetic control efficiently integrates linear regressions across cities for policy influence analysis. Neural networks, suitable for complex systems, operate as black boxes that lack transparency. System dynamics, widely recognized for studying regional development, was employed herein to illustrate feedback loops, and our understanding of the system dynamics was enhanced through causal and flow diagrams. Our study outlines the steps involved in constructing a system dynamics model, encompassing the definition of the research scope and data sources, the selection of indices, the calculation of CCC for urban areas, the construction of the system dynamics model, and settings for the scenario simulations. The system dynamics modeling in this study was built using Vensim PLEx32 7.0 software.

Based on Section 4.2, we sorted the causal relationships among the system elements and depicted the future dynamic process of the influence of innovative resources on the CCC of urban agglomerations. A causal relationship diagram was constructed, wherein the parameters are enclosed in sharp brackets < > and indicated in gray, representing shadow variables appearing multiple times (Figure 2).

Upon examining the causal loops associated with innovative resources, we discern that patent applications authorized, education public budget expenditure, and internal R&D expenditure are the originating factors. Firstly, the surge in patent authorization volume augments valid invention patents, thereby enhancing both IRCC and CCC. Similarly, education public budget expenditure accelerates university development, attracting educators and nurturing research talents, which subsequently reinforces IRCC and CCC. Moreover, it fosters digital talents and expands R&D employment, further elevating competitiveness. Meanwhile, internal R&D expenditure in particular drives R&D job growth, nurtures research talents, and encourages the emergence of digital talents, all of which have a positive impact on IRCC and CCC. Furthermore, these pathways collectively illustrate how investments in research, education, and technological advancements fortify a region’s overall competitiveness and capacity.

Table 2. Feedback loops for innovative resources.

Category	Variables
Patent applications authorized Loop 1	Patent application authorization volume → number of valid invention patents → IRCC → CCC
Education public budget expenditure Loop 1	Education public budget expenditure → university construction → college teachers → scientific research talents → IRCC → CCC
Education public budget expenditure Loop 2	Education public budget expenditure → digital talents → IRCC → CCC
Education public budget expenditure Loop 3	Education public budget expenditure → R&D employment numbers → IRCC → CCC
Education public budget expenditure Loop 4	Education public budget expenditure → scientific research talents → IRCC → CCC
Education public budget expenditure Loop 5	Education public budget expenditure → PSCC → CCC
Public budget expenditure for science and technology Loop 1	Public budget expenditure for science and technology→ digital talents → IRCC → CCC
Public budget expenditure for science and technology Loop 2	Public budget expenditure for science and technology→ PSCC → CCC
Internal R&D expenditure Loop 1	Internal R&D expenditure → R&D employment numbers → IRCC → CCC
Internal R&D expenditure Loop 2	Internal R&D expenditure → scientific research talents → IRCC → CCC
Internal R&D expenditure Loop 3	Internal R&D expenditure → digital talents → IRCC → CCC

lists eleven causal loops related to innovation resources, all of which are reinforcing loops. This indicates that patent applications authorized, education public budget expenditure, internal R&D expenditure, and public budget expenditure for science and technology will influence valid invention patents, talent cultivation, and university development, thereby exerting an influence on IRCC or PSCC and further enhancing CCC.

Based on the causality analysis, we explored practical issues related to system operation and drew a detailed flowchart (Figure 3). This diagram illustrates the interaction paths between various elements in the system, involving 54 variables. Specifically, there are 3 state variables representing different states or conditions during system operation, 48 auxiliary variables providing the necessary information and support for various components of the system, 2 flow variables measuring the speed and volume of the data flow within the system, and 1 constant-a fixed and unchanging numerical value used to maintain balance during the calculation process.

Based on the above flowchart, a cross-interaction relationship exists between these 54 variables, and parameter equations must be set up for these variables to accurately measure the relationships between the system elements. Owing to the similar approach to the parameter settings and equation selection for different regions, we have only listed the calculation equations and main basis for each parameter in Shanghai. When dealing with parameters related to the three types of control variables (ECC, PSCC, and NRCC), we used historical data regression analysis or references to national development plans. For parameters with significant numerical differences across different regions and years and unclear overall patterns, the function with the highest goodness of fit by region was selected for processing. Owing to the complexity and uncertainty of the elements involved in this study, we optimized the set parameter equations repeatedly through multiple runs and debugging and determined the final parameter settings through simulation (

Table 3. Main parameters equation of the CCC system.

Variable	Abbreviations	Unit	Equation	Basis
GDP	GDP	108 yuan	Ramp function	14th Five-Year Plan
Total population	TP	104 person	$T{P}_{\mathrm{t}-1}\times (1+BR-MR)+NIP$	General equation
Birth rate	BR	‰	$0.07\times power(0.990,(Time-2018))$	Select the function with the highest goodness of fit by region
Mortality rate	MR	‰	Regional average	The level within the region is relatively stable.
The proportion of added value of the secondary industry in GDP	PSIG	%	$0.298\times Power(0.960,(Time-2018))$	Select the function with the highest goodness of fit by region
The proportion of added value of the tertiary industry in GDP	PTIG	%	$0.699\times Power(1.015,(Time-2018))$	Select the function with the highest goodness of fit by region
Disposable income of urban residents	DIUR	yuan	$0.096\times percapitaGDP+24984$	The results of linear regression based on historical data
Completed housing area of real estate development enterprises	CHRE	104 m2	After 2020, a 5% decrease annually	The positioning of “housing is for living in, not for speculation” in the 14th Five−Year Plan and the current situation for China’s population
Total profit	TP	108 yuan	$\begin{array}{l}36.491\times PSIG+38.443\times PTIG-36.680\times RDE\\ +1.173\times RDFE+0.011\times MBI-3459.031\end{array}$	Linear regression, with independent variables referencing existing literature (Jiang, 2012) [67]
Savings deposit balance	SDB	108 yuan	$2913.910\times Power(1.001,(Time-2016))$	Select the function with the highest goodness of fit by region
Total sales of wholesale and retail goods above quota	TSWR	108 yuan	The annual growth rate is 8%	14th Five-Year Plan and historical data
Average salary of urban on-the-job employees	ASIE	yuan	The annual growth rate is 8%	14th Five-Year Plan and historical data
Road area proportion	RAP		Cities with a population under 2 million: 0.115; cities with a population over 2 million: 0.175	Referencing existing literature (Wang, 2014) [68]
Increment of park green space area	IPGS	km2	Setting multipliers based on regions for population growth	Referencing existing literature (Du and Liu, 2022) [69]
Attrition of public library books	APLB	104 copies	$0.035\times NAP{L}_{t-1}$	Survey results of multiple libraries
Number of newly acquired public library books	NAPL	104 copies	Calculating the average value by region	Regional historical data
Number of healthcare personnel in hospitals and health centers	NHPH	person	$0.009\times HE+8723.594$	The results of linear regression based on historical data
Health expenditure	HE	104 yuan	$\begin{array}{l}IFTHENELSE(Time<2020,\\ 0.060\times FE,0.070\times FE)\end{array}$	Historical data and IF function by regions
Fiscal expenditure	FE	104 yuan	$\begin{array}{l}IFTHENELSE(Time<2020,\\ 0.280\times GDP,0.300\times GDP)\end{array}$	Historical data and IF function by regions
Education public budget expenditure	EPBE	104 yuan	$\begin{array}{l}IFTHENELSE(Time<2020,0.355\times FE\\ +120.350,0.350\times FE+399.950)\end{array}$	Historical data and IF function by regions
Public budget expenditures for science and technology	PBSD	104 yuan	$\begin{array}{l}0.038\times FE+9819.421\times PTIG\\ -930830\end{array}$	The results of linear regression based on historical data
Built-up area	BUA	km2	$1237.850+(Time-2016)\times 12.379$	The results of linear regression based on historical data
Harmless treatment rate of household waste	HTHW	%	$IFTHENELSE(Time>2016,100,99)$	Historical data and IF function by regions
Centralized treatment rate of sewage treatment plants	CTST	%	$92.800+(Time-2018)\times 0.100$	The results of linear regression based on historical data
Per-unit-value sulfur dioxide emissions in secondary industry	SDES	ton	0.98 times the value of the previous year	Historical data trend
Per-unit-value smoke and dust emissions in secondary industry	ESDS	ton	0.007	The fluctuation range of the data is small, so take the average value
College teachers	NFTH	person	$\begin{array}{l}0.040\times HEF-0.0001\times HEIR\\ +124.726\end{array}$	The results of linear regression based on historical data
Employment in scientific research and technology services	EST	104 people	$\begin{array}{l}(0.106\times RDFE+652.312\times CT+123.833\\ \times EPBE-28868.510)\times 0.010\end{array}$	The results of linear regression based on historical data
Employment in information transmission, software, and information technology services	EISI	104 people	$\begin{array}{l}(0.027\times RDFE+1.083\times ASIE-77132.730)\\ \times 0.010\end{array}$	The results of linear regression based on historical data
Number of R&D personnel	NRDP	person	$\begin{array}{l}(0.027\times RDFE+1.083\times ASIE\\ -77132.730)\times 0.010\end{array}$	The results of linear regression based on historical data
The number of valid invention patents	NVIP	term	$0.680\times PAAV-134$	The results of linear regression based on historical data
Revenue from the sales of new products	RSNP	104 yuan	$320.458+0.560\times NVIP$	The results of linear regression based on historical data
Main business income	MBI	104 yuan	$1.071+0.473\times RSNP$	The results of linear regression based on historical data

).

Additionally, the four IRCC parameters of the number of ordinary higher education institutions and research institutes (HEIR), the expenditure of higher education institutions (EHEI), internal R&D expenditure (RDE), and patent application authorization volume (PAAV) have not set equations. This is because the subsequent scenario simulation settings need to directly set equations for these four innovative resources and analyze their future influence on CCC trends.

4.4. Scenario Simulation Settings

To gain a deeper understanding of the long-term influence of innovative resources on CCC, we assume that certain types of innovative resources will be enhanced while the general indicators will continue following their historical trends. We designed five development scenarios to predict the future influence of different types of innovative resources on CCC. Through comparative analysis, we found that increasing expenditure and patent applications effectively enhances the CCC of urban agglomerations. Nevertheless, the excessive expansion of universities and research institutions may hinder CCC’s improvement. Taking Shanghai, Qingdao, and Guangxi as examples, the simulation results obtained through Vensim PLEx32 7.0 software indicate that when the number of ordinary higher education institutions and research institutes increases by 20% while the other indicators remain unchanged according to their current trends, the CCC will decrease by nearly 6%, 7%, and 11%, respectively, by 2040. Consequently, these five innovative resource development scenarios vary in the expenditure levels of higher education institutions (EHEI), internal R&D expenditure (IRDE), and patent application authorization volume (PAAV).

The five scenarios proposed are as follows: Scenario 1, also known as the current scenario, maintains the current status of higher education institutions (EHEI), internal R&D expenditure (IRDE), and patent application authorization volume (PAAV) until 2040. Scenario 2, the 5% scenario, assumes a 5% increase in the development levels of EHEI, IRDE, and PAAV. Scenario 3, the 10% scenario, envisages a 10% increase in these indicators. Similarly, Scenario 4 represents a 15% increase in these three indicators, whereas Scenario 5 assumes a 20% increase.

5. Analysis of the Results

5.1. Analysis of Model Testing Results

The first step was to verify historical data (2011–2020). The simulated and real data for the five criteria layers in Shanghai were compared (Figure 4). From the curve, it can be observed that the trends in the simulated and real values over time are relatively consistent, and the values are also consistent. Among the 50 simulated values, the average error was 3.7%, and only two years had a difference of more than 10% in their economic carrying capacity (11% and 12%, respectively). All the simulated values met the standard of having an average error within 10–15%. Based on historical data testing, evidently, the system dynamics model developed in this study demonstrates an appropriate fit, accurately reflecting the operational principles of the system in a scientifically sound manner.

Step 2 involved extreme condition testing. This testing method sets certain variables in the model as extreme values, observes the changes in the simulation system, and evaluates whether the constructed model conforms to the actual situation. When we set the birth rate and initial variables of Shanghai to 0, the per capita GDP tends toward infinity, as does the economic carrying capacity. This result is logically reasonable.

In summary, the simulation model of the CCC system passed the tests with historical data and extreme conditions. Establishing a system simulation model requires continuous adjustment and optimization based on the historical data of all variables to enable the determined model to be closer to the actual situation naturally.

5.2. Analysis of Historical Data Revealing Innovative Resources’ Influence

To visually demonstrate the relationship between innovative resources and CCC within China’s urban agglomerations, we combined historical data from the 2020 IRCC and CCC values of 31 core cities within 19 urban agglomerations to create a map. This map was created using ArcGis10.7 software and the means of the five-fifths method [70]. IRCC and CCC were ranked according to five levels in sequence from lowest to highest, and distinct colors were used to differentiate between the various levels (Figure 5).

The IRCC and CCC levels exhibited a highly consistent trend. From a statistical perspective, IRCC significantly positively influences CCC, indicating that CCC is also relatively high in regions with higher levels of innovative resources. This observation is consistent with the conclusions of the theoretical model and the problem hypothesis, further confirming this theory’s effectiveness. From a single urban agglomeration perspective, innovative resources are predominantly concentrated in cities within national-level urban agglomerations, such as Beijing–Tianjin–Hebei, the Yangtze River Delta, and the Pearl River Delta. These urban agglomerations have relatively complete scientific and technological innovation systems and high-quality talent resources and a high level of economic development and a high-quality social environment. Some cities in regional urban agglomerations in the central and western regions, such as the Chengdu–Chongqing economic zone, Central China, and the city of Wuhan in the Middle reaches of the Changjiang River, also performed well in terms of IRCC and CCC; the regional-level urban agglomerations in the northeast and western regions lack innovative resources, possibly attributable to their relatively lagging economic development, talent loss, and a lack of educational and medical resources. Noteworthily, although the West Coast of Taiwan Strait has a relatively high economic development level, its IRCC and CCC are relatively low. The main reasons for this are the small built-up area, the small road area, and fewer people engaged in scientific and technological research and development, precipitating a limited carrying capacity.

5.3. Analysis of the Predicted Data Revealing the Influence of Innovative Resources on CCC

This study comprehensively considered the CCC levels of urban agglomerations and selected data from Shanghai, Qingdao, and Xining from 2011 to 2040 for the next simulation prediction. Shanghai—as the core of the Yangtze River Delta urban agglomeration—has the strongest comprehensive strength and the highest economic share among the national-level urban agglomerations. Qingdao is at the core of the Shandong Peninsula urban agglomeration, with an important geographical location that connects multiple regions. Xining is the core of the Lanxi urban agglomeration, with an optimized industrial structure adjustment but a low development level, a fragile environment, and prominent problems in small towns. On the premise of passing the requisite tests, this study combined the system flowchart (Figure 3) and parameter equation (Table 3), inputted the variables and equations into the Vensim PLEx32 7.0 software, simulated the dynamic evolution brought about by system operation, and combined it with the actual situation of innovative resources and CCC. After multiple repeated experiments, the simulation time range was set to 2011–2040, with a total duration of 30 years and a step size of 1 year (Figure 6).

Figure 6 depicts the CCC simulation results for Shanghai, Qingdao, and Xining from 2011 to 2040. The corresponding curve exhibits the trend in the CCC over time. From a time trend perspective, irrespective of whether innovative resource optimization is implemented, the numerical value of CCC exhibits an increasing trend year by year. This phenomenon proves that China has entered a new stage of high-quality development, and the coordinated development levels of society, resources, and the economy are continuously improving.

Compared to the current scenario, the optimization of innovative resources in these three cities can result in varying degrees of CCC improvement, which aligns with existing research indicating that innovation activities can improve economic growth, pollution control, transportation, communication, infrastructure, and enterprise operations [34,35,36,37,38,39,40,41]. According to Figure 6a, the simulation results for Shanghai’s CCC in 2040 are as follows: about 2 under the current scenario, about 3 under the scenario of 10% optimization, about 7 under the scenario of 15% optimization, and about 18 under the scenario of 20% optimization. This indicates that optimizing innovative resources is an effective means for Shanghai to improve its CCC; moreover, when the optimization of innovative resources reaches a certain level, it will achieve a qualitative leap in its comprehensive carrying structure. Per Figure 6b, the simulation results for Qingdao’s CCC in 2040 are as follows: about 0.8 under the scenario of no optimization of innovative resources, about 1 under the scenario of 10% optimization, about 1.8 under the scenario of 15% optimization, and about 4.5 under the scenario of 20% optimization. This indicates that although the effect of innovative resource optimization in Qingdao on promoting the CCC is relatively limited compared to that in Shanghai, optimizing innovative resources is still an effective way to improve CCC; especially when the optimization degree reaches 15% or more, the optimization effect is significant. Similarly, the effect of innovative resource optimization on promoting the CCC in Xining, as presented in Figure 6c, is similar to that in Qingdao. At this point, it is evident that optimizing the allocation of innovative resources is an effective means for China’s urban agglomerations to achieve positive changes in their CCC structure.

6. Conclusions and Policy Implications

The CCC of urban agglomerations is influenced by the synergistic effects of multiple factors that form a complex system coupled with multiple factors, which contains a large number of linear and nonlinear relationships. This comprehensive study employs a multifaceted strategy, integrating system dynamics modeling for dynamic simulations, a literature analysis for theoretical grounding, theoretical insights for conceptual clarity, and statistical analysis for empirical validation. Its goal is to thoroughly apply the CCC evaluation framework, incorporating data calculation and predictive simulations while emphasizing the optimization of innovative resources. By harmoniously combining these methodologies, this study endeavors to gain a deeper understanding of how augmenting innovative resources can propel sustainable urban development and bolster the resilience of urban agglomerations, fostering long-term prosperity and adaptability. Specifically, the research underscores a correlation between the CCC framework and the improvement of innovative resources within urban agglomerations (

Table 4. Research contents indicate that innovative resources have a positive influence on CCC.

Research Contents	Time Frame of the Section	Research Methods	Conclusions
Section 2.3	References within the most recent years	literature analysis	Innovative resources positively influence economic growth, pollution control, transportation, communication, infrastructure, and enterprise operations
Table 3: Main parameters in equations for the CCC system	2011–2040	Refer to14th Five-Year Plan, historical data, linear regression, existing literature, the highest goodness function, etc.	There exists a correlation between the parameters of innovative resources and other parameters related to CCC
Section 5.2	2020	Statistical methods	IRCC significantly positively influences CCC
Section 5.3	System dynamics	System dynamics methods	Optimizing the allocation of innovative resources is an effective means for China’s urban agglomerations to achieve positive changes in their CCC structure

).

Based on the conclusions drawn from the research, we propose the following policy implications. The central government should strengthen the top-level design of innovative resource allocation between and within urban agglomerations and focus on regional urban agglomerations with scarce resources. National-level urban agglomerations should promote the sharing and exchange of innovative resources and contribute to their leading global position. Less developed areas should optimize their resource allocation structures and take advantage of strategic opportunities to overcome and solve urban problems.

In the context of the diminishing comparative advantage of traditional resources, the comparative advantage of innovative resources is becoming an important driving factor in reshaping the CCC structures and enhancing the carrying capacity of global urban agglomerations. National-level urban agglomerations should strengthen policy guidance and their technological drive; deepen the industrial chain; and enhance high-end, intelligent, and green development. Resource-based regional urban agglomerations must optimize industrial innovation ecology, reduce resource development pressure, and help achieve carbon goals. Manufacturing-led urban clusters must promote industrial transformation and shift toward knowledge-intensive industries. During the cultivation period, regional urban agglomerations should accurately match innovative human resources, introduce professional talents, enhance the attractiveness of high-level talents, and assist in the technological self-reliance and modernization of industrial system construction.

The government and society should increase expenditure on universities and research institutes and optimize innovative resources. The government should increase the budget for the education sector, establish special expenditures for higher education, and encourage social donations. Technology-oriented enterprises should set clear research expenditure goals; establish scientific budgeting, approval, and performance evaluation mechanisms; improve utilization efficiency; and seek external financial support.

Simply increasing the number of universities and research institutes cannot effectively improve innovative resources, which may precipitate resource dispersion and inefficient utilization. Innovative talents form the core element, and human capital with heterogeneous skills achieves market equilibrium through agglomeration effects. It is necessary to encourage risk-taking; tolerate failure; and solve the problems of examination-oriented education, a lack of innovation, and talent loss abroad.

Effective invention patents are the key to enhancing the CCC of urban agglomerations, and it is necessary to establish a patent application support mechanism and a patent reward system and improve intellectual property laws and regulations. Simultaneously, policy design should encourage high-quality innovation and guide enterprises to engage in high-risk but promising innovations.

A virtuous cycle exists between higher education funding, internal research funding within enterprises, and effective invention patents. Funding from investment promotes scientific research optimization and improves resource quality and internal investment to support innovation and R&D within an enterprise. Innovative achievements bring economic returns through patent protection, attract investment and cooperation, further increase funding investment, and form a virtuous cycle.

However, this study aims to contribute to the field by exploring the role of innovative resources in enhancing the CCC of urban agglomerations. By analyzing the influence of innovation on various aspects of urban development, it lays the groundwork for future research in this domain. While further research is needed to delve into the synergies between innovative resources and three subsystems, economic carrying capacity (ECC), public service carrying capacity (PSCC), and natural resource carrying capacity (NRCC), this study has not extensively explored the interconnections among these subsystems. The aim is to gain a holistic understanding of urban agglomerations’ carrying capacity, which is essential for realizing their modernized and sustainable development.