Discrete Dynamics in Nature and Society

Coal-resource-based cities, as one of the important types of typical resource-based cities in China, have strong characteristics of instability, sensitivity, and fragility, exhibiting a series of vulnerability features of the human-land system. Previous studies have lacked a deeper investigation into the vulnerability of such cities from the perspective of coupling feedback mechanisms among various elements or subsystems. This paper adopts Bohle et al.’s “Dual Structure Model” of vulnerability to establish an indicator system for vulnerability warning in coal-resource-based cities. Using Fushun City as a sample, a dynamic simulation model of vulnerability in coal-resource-based cities is constructed based on system dynamics for warning simulation calculations, analyzing the evolution trend of vulnerability in Fushun City from 2010 to 2022. The results show the following: (1) from 2010 to 2022, the urban vulnerability of Fushun City transitioned from a medium warning level to a relatively safe level, showing a trend of annual reduction and improvement, undergoing three development stages of significant reduction, fluctuation stabilization, and slight rebound. (2) Due to the causal relationships among various elements within the vulnerability subsystems of Fushun City, differences exist in the contribution levels of vulnerability subsystems during the period 2010–2022, under the combined effects of sensitivity and adaptability factors. The contribution rate of the natural subsystem was the highest from 2010 to 2014, while, from 2016 to 2019, urban vulnerability began to shift towards an economically and socially dominant type. Influenced by the pandemic, Fushun City’s overall vulnerability has shown an upward trend since 2020 compared to the previous stage. Finally, specific policy suggestions are proposed for Fushun City to cope with vulnerability changes based on the analysis results, providing a theoretical basis for achieving sustainable development in such coal-resource-based cities.

Under the influence of the COVID-19, great changes have taken place in China’s economic structure and market subjects and college students are facing difficulties in employment. By carrying out collaborative innovation between schools and enterprises, cultivating high-quality talents to meet social needs has become an important way to solve difficulties. Based on the input-process-output principle, a performance evaluation index system for collaborative innovation is constructed, which includes 3 primary indicators and 22 secondary indicators. The weights of each indicator are determined using improved AHP. A mathematical model for evaluating the performance of school enterprise collaborative innovation is established using the fuzzy comprehensive evaluation method. The evaluation value of the innovation and entrepreneurship education case project is 0.82, indicating that the overall operation is in good condition. The cooperation between schools and enterprises has created a favorable atmosphere and accumulated rich experience for carrying out innovation and entrepreneurship education. Good results have been achieved in talent cultivation and scientific and technological output, but there are also problems such as low conversion rates of scientific and technological achievements. Based on the evaluation results, the article proposes suggestions to improve the performance of collaborative innovation between schools and enterprises. The research results provide theoretical reference for the performance evaluation of school enterprise collaborative innovation and the practice of innovation and entrepreneurship education.

Connected and automated vehicles can reduce the traffic congestion level of the entire network through platoon-driving technologies compared to human-driven vehicles. One promising approach to enhancing platoon-driving technology’s efficiency is deploying dedicated lanes or roads for connected and automated vehicles. Since asymmetric interactions between different vehicle types increase road congestion, it is necessary to distinguish routes for efficient traffic management. However, the traditional traffic assignment problem, which uses only user equilibrium as a constraint with no difference in travel time between users, could not be proposed as a globally optimal solution because it generates an infinite number of locally optimal solutions. Recent studies have attempted to overcome the limitations by considering the sum of system-wide travel times as an additional constraint. Their research sought to help propose optimal deployment strategies through the lowest total travel time solution (best-case) or design robust transport planning strategies through the highest total travel time solution (worst-case). However, past studies have not focused on the possibility of the best/worst case appearing in reality. This study focused on the relationship between the two solutions pointed out in past studies and traffic patterns likely to appear in reality. This study interprets the Karush–Kun–Tucker condition of the static traffic assignment problem, considering the asymmetric interaction, and proposes a solution algorithm using discrete dynamics. The proposed algorithm extends the most widely used method in transportation planning research, which can overcome the limitations of asymmetric interaction problems through simple variations. The proposed algorithm can reliably derive two solutions, and entropy theory shows that both solutions are unlikely to appear in reality without additional policies such as dedicated lanes or roads.

In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number . The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if , then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst , the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.

The development of the textile and apparel (T&A) industry has led to an increasing focus on recycling used products. Remanufactured product quality raises consumer concerns, and blockchain can effectively solve this problem. We establish a closed-loop supply chain (CLSC) in which a manufacturer, a retailer, or a third-party recycler collects used T&A products to examine the most efficient recycling mode with and without blockchain and the impact of blockchain on CLSC decisions. The results show that (1) if the manufacturer’s recycling cost coefficient is relatively low, used T&A products are collected directly by the manufacturer. Otherwise, the responsibility for recycling used T&A products falls to the retailer or the third-party recycler. It is noteworthy that the manufacturer’s choice of recycling mode remains unchanged whether a blockchain is implemented or not. (2) The implementation of blockchain by the manufacturer and the retailer can increase profits and consumers also benefit when the cost of validating blockchain units remains below a certain threshold. (3) When the recycling cost coefficient exceeds a certain threshold, the implementation of blockchain increases prices and recycling rates. These findings offer CLSC members’ management insights into how to select the optimal recycling mode and the consequences of implementing blockchain.

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.