Search Results (149)

This study extends the post-Keynesian framework for cyclical economic growth, initially proposed by Goodwin in 1967, by integrating government intervention to stabilize employment amidst wage mismatches. Given the pressing challenges of unemployment and wage disparity in developing economies, particularly South Africa, this extension is necessary to better understand how policy interventions can influence labor market dynamics. Central to the study is the endogenous interaction between capital and labor, where class dynamics influence economic growth patterns. The research focuses on the competitive relationship between real wage growth and its effects on employment. Methodologically, the study measures the impact of intervention strategies using a system of coupled ordinary differential equations (Lotka–Volterra type), along with econometric techniques such as quantile regression, moving averages, and mean absolute error to measure wages mismatch. Results demonstrate the inherent contradictions of capitalism under intervention, confirming established theoretical perspectives. This work further contributes to economic optimality discussions, especially regarding the timing and persistence of economic cycles. The model provides a quantifiable approach for formulating intervention strategies to achieve long-term economic equilibrium and sustainable labor–capital coexistence. Full article

A Lotka–Volterra-type system with porous diffusion, which can be used as an alternative model to the classical Lotka–Volterra system, is under study. Multiparameter families of exact solutions of the system in question are constructed and their properties are established. It is shown that the solutions obtained can satisfy the zero Neumann conditions, which are typical conditions for mathematical models describing real-world processes. It is proved that the system possesses two stable steady-state points provided its coefficients are correctly specified. In particular, this occurs when the system models the prey–predator interaction. The exact solutions are used for solving boundary-value problems. The analytical results are compared with numerical solutions of the same boundary-value problems but perturbed initial profiles. It is demonstrated that the numerical solutions coincide with the relevant exact solutions with high exactness in the case of sufficiently small perturbations of the initial profiles. Full article

In the digital transformation era, understanding the relationship between digital and real economies is vital for regional development. This study analyses the interaction between these two economies in Henan Province using panel data from 18 cities (2011–2023). It incorporates policy support intensity through fuzzy set theory, applies an integrated weighting method to measure development levels, and uses regression models to assess the digital economy’s impact on the real economy. The coupling coordination degree model, kernel density estimation, and Gini coefficient reveal the coordination status and spatial distribution, while the ecological Lotka–Volterra model identifies the symbiotic patterns. The key findings are as follows: (1) The digital economy does not directly determine the state of the real economy. For example, cities such as Zhoukou and Zhumadian have low digital economy levels but high real economy levels. However, the development of the digital economy promotes the real economy without signs of diminishing returns. (2) The two economies are generally coordinated but differ spatially, with greater coordination in the Central Plains urban agglomeration. (3) The digital and real economies exhibit both collaboration and competition, with reciprocal mutualism as the dominant mode of integration. These insights provide guidance for policymakers and offer a new perspective on the integration of both economies. Full article

In ecosystems, spatial structure plays a fundamental role in shaping the observed dynamics. In particular, the availability and distribution of unoccupied sites—potential habitats—can strongly affect species persistence. However, mathematical models of ecosystems based on ordinary differential equations (ODEs) often neglect the explicit representation of these unoccupied sites. Here, probabilistic cellular automata (PCA) are used to reproduce two basic ecological scenarios: competition between two species and a predator–prey relationship. In these PCA-based models, unoccupied sites are taken into account. Subsequently, a mean field approximation of the PCA behavior is formulated in terms of ODEs. The variables of these ODEs are the numbers of individuals of both species and the number of empty cells in the PCA lattice. Including the empty cells in the ODEs leads to a modified version of the Lotka–Volterra system. The long-term behavior of the solutions of the ODE-based models is examined analytically. In addition, numerical simulations are carried out to compare the time evolutions generated by these two modeling approaches. The impact of explicitly considering unoccupied sites is discussed from a modeling perspective. Full article

Mathematical modeling plays a crucial role in supporting decision-making across a wide range of scientific disciplines. These models often involve multiple parameters, the estimation of which is critical to assessing their reliability and predictive power. Recent advancements in artificial intelligence have made it possible to efficiently estimate such parameters with high accuracy. In this study, we focus on modeling the dynamics of cryptocurrency market shares by employing a Lotka–Volterra system. We introduce a methodology based on a deep neural network (DNN) to estimate the parameters of the Lotka–Volterra model, which are subsequently used to numerically solve the system using a fourth-order Runge–Kutta method. The proposed approach, when applied to real-world market share data for Bitcoin, Ethereum, and alternative cryptocurrencies, demonstrates excellent alignment with empirical observations. Our method achieves RMSEs of 0.0687 (BTC), 0.0268 (ETH), and 0.0558 (ALTs)—an over 50% reduction in error relative to ARIMA(2,1,2) and over 25% relative to a standard NN–ODE model—thereby underscoring its effectiveness for cryptocurrency-market forecasting. The entire framework, including neural network training and Runge–Kutta integration, was implemented in MATLAB R2024a (version 24.1). Full article

In this integrative review paper, we explore the parallels between the physical models of gyrotrons and some equations used in diverse and broad scientific fields. These include Adler’s famous equation, Van der Pol equation, the Lotka–Volterra equations and the Kuramoto model. The paper is written in the form of a pedagogical discourse and aims to provide additional insights into gyrotron physics through analogies and parallels to theoretical approaches used in other fields of research. For the first time, reachability analysis is used in the context of gyrotron physics as a modern tool for understanding the behavior of nonlinear dynamical systems. Full article

Regulating lamprey populations is crucial for maintaining ecological equilibrium. However, the unique sex determination process of lampreys is constrained by multiple factors, complicating intuitive analysis of population dynamics and their impact on the natural environment. This study employed a two-species competition mechanism to elucidate the factors influencing sex ratios and their mechanistic effects on lamprey population size. Using the Lotka–Volterra equations, we investigated how sex ratios affect trophic levels both upstream and downstream of lampreys in the food web. A logistic population growth model was applied to assess the impact of sex ratio variations on symbiotic parasitic species, while the Analytic Hierarchy Process (AHP) was utilized to explore the dynamic relationship between sex ratio changes and ecosystem stability. To validate model efficacy, we manipulated temperature and food availability under controlled disturbance conditions, analyzing temporal variations in lamprey population size across different disturbance intensities to evaluate model sensitivity. The findings indicate that the variable sex ratio’s benefit is in facilitating the lampreys’ population’s enhanced adaptation to environmental shifts. The coexisting species exhibit a similar pattern of population alteration as the lampreys, albeit with a minor delay. A definitive link between the quantity of lampreys and the parasitic species is absent. A male ratio of 0.6 optimally contributes to the ecosystem’s equilibrium. Over time, the configuration of our model’s parameters proves to be sensible. This research provides robust theoretical support for developing scientific strategies to regulate lamprey populations. Full article

With the shift of the global innovation model from traditional closed-loop to open ecosystems, knowledge sharing and collaborative cooperation among firms have become key to obtaining sustainable competitive advantages. However, existing studies mostly focus on the static structure, and there is an insufficient exploration of the dynamic evolutionary mechanism and multi-party game strategies. In this paper, a two-dimensional analysis framework integrating the evolutionary game and the Lotka–Volterra model is constructed to explore the behavioral and strategic evolution of core enterprises, SMEs and the government in the innovation ecosystem. Through theoretical modeling and numerical simulation, the effects of different variables on system stability are revealed. It is found that a moderately balanced benefit allocation can stimulate two-way knowledge sharing, while an over- or under-allocation ratio will inhibit the synergy efficiency of the system; a moderate difference in the knowledge stock can promote knowledge complementarity, but an over-concentration will lead to the monopoly and closure of the system; and the government subsidy needs to accurately match the cost of the openness of the enterprises with the potential benefits to the society, so as to avoid the incentive from being unused. Accordingly, it is suggested to optimize the competition structure among enterprises through the dynamic benefit distribution mechanism, knowledge sharing platform construction and classification subsidy policy, promote the evolution of the innovation ecosystem to a balanced state of mutual benefit and symbiosis, and provide theoretical basis and practical inspiration for the governance of the open innovation ecosystem. Full article

This study investigates a modified Lotka–Volterra commensalism system that incorporates the weak Allee effect in prey and symmetric (equal harvesting effort for both species) non-selective harvesting, addressing a critical gap in ecological modeling. Unlike previous work, we rigorously examine how the interaction between the Allee effect and harvesting disrupts system stability, giving rise to novel bifurcation phenomena and population collapse thresholds. Using eigenvalue analysis and the Dulac–Bendixson criterion, we derive sufficient conditions for the existence and stability of equilibria. We find that harvesting destabilizes the system by inducing two saddle-node bifurcations. Notably, prey abundance can increase with greater Allee intensity under controlled harvesting—a rare and counterintuitive ecological outcome. Moreover, exceeding a critical harvesting threshold drives both species to extinction, while controlled harvesting allows sustainable coexistence. Numerical simulations support these analytical findings and identify critical parameter ranges for species coexistence. These results contribute to theoretical ecology and offer insights for designing sustainable harvesting strategies that balance exploitation with conservation. Full article

This study investigates the evolutionary mechanisms and equilibrium character-istics of the China–US trade dispute through an improved ecological competition model. By quantifying tariff policies as competition intensity regulators and introducing trade elasticity parameters, we construct a dynamic system that captures the nonlinear feedback between economic rivals. Key findings are as follows. (1) When both nations implement reciprocal tariff measures with similar economic sensitivities, the system converges to a stable equilibrium where bilateral economic outputs stabilize at reduced levels compared to pre-conflict states, provided the product of adjusted competition coefficients remains below critical thresholds. (2) Excessive tariff escalation beyond identifiable tipping points triggers winner-takes-all outcomes, validating the “Thucydides Trap” hypothesis in eco-nomic conflicts. (3) Empirical simulations using 2018–2023 trade data demonstrate that China’s tit-for-tat tariff strategy effectively maintains competitive balance, while domestic market expansion measures (evidenced by a 6.3% average annual growth in China’s do-mestic consumption) significantly mitigate trade diversion effects. The study establishes theoretical connections with optimal tariff theory and strategic trade policy literature while providing policymakers with quantitative tools to assess trade policy impacts. Our find-ings theoretically validate China’s policy combination of calibrated reciprocity and domestic demand stimulation, offering new insights into managing great-power economic competition. Full article

Neural Ordinary Differential Equations (Neural ODEs) have emerged as a promising approach for learning the continuous-time behaviour of dynamical systems from data. However, Neural ODEs are black-box models, posing challenges in interpreting and understanding their decision-making processes. This raises concerns about their application in critical domains such as healthcare and autonomous systems. To address this challenge and provide insight into the decision-making process of Neural ODEs, we introduce the eXplainable Neural ODE (XNODE) framework, a suite of eXplainable Artificial Intelligence (XAI) techniques specifically designed for Neural ODEs. Drawing inspiration from classical visualisation methods for differential equations, including time series, state space, and vector field plots, XNODE aims to offer intuitive insights into model behaviour. Although relatively simple, these techniques are intended to furnish researchers with a deeper understanding of the underlying mathematical tools, thereby serving as a practical guide for interpreting results obtained with Neural ODEs. The effectiveness of XNODE is verified through case studies involving a Resistor–Capacitor (RC) circuit, the Lotka–Volterra predator-prey dynamics, and a chemical reaction. The proposed XNODE suite offers a more nuanced perspective for cases where low Mean Squared Error values are obtained, which initially suggests successful learning of the data dynamics. This reveals that a low training error does not necessarily equate to comprehensive understanding or accurate modelling of the underlying data dynamics. Full article

Diversification and business expansion have become key strategies for modern business development, prompting many large companies to move from singular service models to diversified service strategies, ultimately evolving into comprehensive service ecosystems. Therefore, an in-depth understanding of the evolutionary patterns of service ecosystems is crucial for formulating efficient and effective management strategies and helping enterprises to make informed decisions during the service innovation process. At present, research on the evolution of service ecosystems largely lacks sufficient theoretical underpinning and focuses on the supply–demand relationship relationship, which reduces the credibility of research conclusions and ignores the influence of multiple factors. In this paper, the Lotka–Volterra (LV) model is introduced to service ecosystems and the model as a ternary framework that captures competition–cooperation dynamics among atomic and composite services. In addition, an agent-based computational experiment is designed to integrate adversarial games for decision-making and genetic algorithms for service evolution. Furthermore, the results indicate that moderate competition $\alpha \approx 0.5$ among atomic services maximizes composite service innovation and excessive cooperation $\alpha \to 0$ stifles it. Full article

Addressing the dual challenges of agricultural productivity and ecological sustainability, this study develops an integrated framework combining Lotka–Volterra dynamics, Monte Carlo simulation, and multi-objective optimisation to quantify agroecosystem responses under anthropogenic interventions. Key innovations include the incorporation of carbon sequestration dynamics and low-carbon agricultural practices into ecological–economic trade-off analysis. Our findings demonstrate the following: (1) Seasonal carbon fertilisation effects enhance producer growth by up to 30%, while energy recycling from consumer mortality offsets 22% of pesticide-induced carbon emissions. (2) The strategic introduction of dual-function species synergistically improves carbon sink capacity by 18–25% through enhanced producer efficiency and reduced chemical reliance. (3) Multi-objective optimisation reveals that integrated pest management coupled with organic amendments achieves a 51.2% net benefit improvement, while reducing agrochemical carbon footprints by 40–55%. The proposed framework bridges critical gaps in sustainable agriculture by simultaneously addressing yield stability, biodiversity conservation, and climate mitigation imperatives. This work advances the dynamic modelling of agroecosystems through probabilistic risk assessment and carbon-aware decision-making, providing actionable pathways for low-carbon agricultural intensification. Full article

High-tech industries are of strategic importance to the national economy, and Beijing has been designated as a science and technology innovation center by the State Council. Accurate analysis of its added value is crucial for technological development. While recent data enhance prediction accuracy, its limited volume poses challenges. The cumulative grey Lotka–Volterra model and grey differential dynamic multivariate model address this by leveraging short-term data effectively. This study applies these two models to analyze influencing factors and predict Beijing’s high-tech industry growth. Results show a competitive relationship with four systems, lacking synergy. In the next five years, a mutually beneficial trend is expected. The Mean Absolute Percentage Error (MAPE) remains within 10%, confirming the model’s reliability. Full article

With the development of new agricultural business entities in China, a complex competitive evolutionary dynamic has emerged among diversified agricultural business entities (abbreviated as ABEs), including farmers (traditional ABEs), cooperatives, agricultural enterprises, and family farms (new ABEs). Based on the Lotka–Volterra model, the dominance index, the Shannon–Wiener index of ecological theories, and the geo-detector, this study examines the spatiotemporal evolution and driving factors of ABEs’ structural changes across 286 Chinese cities from 2012 to 2021. Key findings include: (1) Farmers maintain absolute numerical dominance, but their relative advantage has declined. (2) The Shannon–Wiener index of diversified ABEs has increased significantly, indicating that differences between ABEs decreased, which means a trend toward structural homogenization. High Shannon–Wiener index values were observed in the Northeast Plain, Xinjiang, Hebei, Gansu, and Shanxi, while low values were concentrated in Yunnan, Guizhou, and the Guangdong-Guangxi region. Both areas experienced a shrinking trend. (3) Agricultural production factors such as multiple cropping indexes and theindustrial structure strongly explained the structural changes to ABEs, while the explanatory power of socio-economic factors can be enhanced after the interaction with agricultural production factors. (4) The relationship between farmers and new ABEs has shifted from a symbiotic relationship favoring farmers to a symbiotic relationship favoring new ABEs, with a significant spatial heterogenous layout among 286 cities. This study proposes a three-stage differentiation framework for ABEs: a simple structure dominated by traditional farmers, a competitive evolutionary dynamic among diversified ABEs, and a modernized structure led by new agricultural business entities. Based on these stages, this paper provides targeted recommendations for building a high-quality ABE system and advancing agricultural modernization. Full article