Discrete Dynamics in Nature and Society

This work will study an optimal control problem describing the two-strain SEIR epidemic model. The model studied is in the form of six nonlinear differential equations illustrating the dynamics of the susceptible and the exposed, the infected, and the recovered individuals. The exposed and the infected compartments are each divided into two subclasses representing the first and the second strains. The model includes two saturated rates and two treatments for each strain. We begin our study by showing the well posedness of our problem. The basic reproduction number is calculated and depends mainly on the reproduction numbers of the first and second strains. The global stability of the disease-free equilibrium is fulfilled. The optimal control study is achieved by using the Pontryagin minimum principle. Numerical simulations have shown the importance of therapy in minimizing the infection’s effect. By administrating suitable therapies, the disease’s severity decreases considerably. The estimation of parameters as well as a comparison study with COVID-19 clinical data is fulfilled. It was shown that the mathematical model results fit well the clinical data. In order to eradicate the infection, it is very important that the first and second strain reproduction numbers must be less than unity.

In this paper, chaos of a new exponential logistic map modulated by Gaussian function is investigated. Firstly, the stability of the fixed point is analyzed, and the occurrence of period doubling bifurcation in the system is verified theoretically. Subsequently, the chaotic behavior of the system is analyzed using bifurcation diagrams, phase portraits, and Lyapunov exponents. The numerical results confirm the existence of chaos in the exponential logistic map within a specific parameter range. In addition, the proposed map has additional parameter degrees of freedom compared to the existing generalized logistic maps, which provides different chaotic characteristics and enhances design flexibility required for diverse applications. At last, we further study the two-dimensional coupled exponential logistic map and find that the system enters chaos through two routes: period doubling bifurcation and Hopf bifurcation.

The COVID-19 pandemic is having a significant impact on the financial supply chain (FSC), with the disruption of supply and demand causing economic chaos and business disruption for companies, their customers, suppliers, and related service providers. To mitigate the financial disruption caused by COVID-19, companies are turning to supply chain (SC) financing solutions to stabilize liquidity and maintain solvency. Sustainability in the three dimensions of economy, environment, and society as well as the integration of financial and material flows ensure the long-term survival of an SC. Therefore, this study proposes a model for integrated physical and financial planning of a stable closed-loop supply chain (SCLSC). This model aims to maximize profit, minimize environmental and social impacts, and minimize undesirable deviations of financial indicators from their target level. To cope with the multiple objectives of the model, the goal programming (GP) method was used and the model was implemented during the COVID-19 pandemic in Iran. The proposed model is designed for multiple periods and products. The study proposes a model for financial and physical planning during COVID-19.

Under the influence of the pandemic and economic slowdown, real estate companies are facing severe financial risk, which has become a focal point of widespread concern. This study constructs a financial health evaluation model for real estate development enterprises on the basis of the entropy-VIKOR algorithm. Using China as a case study, this research selects real estate companies listed on the Shanghai and Shenzhen Stock Exchanges before the end of 2016 as the sample for empirical analysis. Sensitivity and validity analyses were conducted using 2020 data to ensure the robustness of the financial health evaluation model. The study identifies accounts receivable turnover and the interest coverage ratio as key secondary indicators of financial health in real estate companies, whereas operational capacity and debt repayment ability are critical primary indicators. The model is insensitive to weight perturbations, suggesting that its evaluation results are valid and predictive. Additionally, the pandemic and changes in the macroeconomic environment have negatively impacted corporate financial conditions, but internal adjustments and optimization strategies have contributed to the recovery of financial health. Finally, we analyze the research findings and provide targeted recommendations, with the aim of enabling real estate enterprises to respond better to macroeconomic and policy changes, thereby enhancing their financial health and market competitiveness.

The dynamic latent space model is widely used in analysing network data. It can provide useful visualization and interpretation of networks, as well as represent the inherent reciprocity and transitivity. In this paper, a dynamic latent space model with position clusters is proposed. The model extends the dynamic latent space model by incorporating latent position clustering and accounting for weighted networks. A fully Bayesian method with adaptive Markov chain Monte Carlo sampling is used to estimate the novel model. A purity-based relabelling algorithm is proposed to resolve label switching. This model can be extended to analyse binary networks, count networks and sparse weighted networks. Finally, the model is used to analyse the product trade data of 54 countries from 2010 to 2019.

At present, the digital transformation in the global economy is accelerating. In order to understand the development of e-commerce in China correctly, the study establishes eight secondary indicators to estimate the level of e-commerce in China from 2013 to 2021 with the entropy weight–CRITIC method. Using the Dagum Gini coefficient, we investigated the overall, intraregional, and interregional differences in the level of e-commerce in China. Through Kernel density estimation and Markov chain analysis, the study explored the dynamic evolution characteristics of their distribution. From 2013 to 2021, the level of e-commerce in China exhibited a fluctuating upward trend, with an overall growth rate of 71.82%, but the overall level of e-commerce was still low, showing a strong presence in the east and a weak presence in the west. It is evident that the differences in the level of e-commerce mainly came from regional variations, with an average contribution rate of 72.98%. From the perspective of the dynamic evolution of distribution, the level of Chinese e-commerce exhibited strong stability and characteristics of club convergence. Considering the spatial factors, the convergence of Chinese e-commerce levels is evident. Based on the results, the study will propose a series of countermeasures and suggestions for adopting a regional coordinated development strategy to reduce the gap in e-commerce levels between different regions.

This study examines the impact of digital transformation in focal enterprises on the carbon emission intensity of upstream and downstream firms within industrial chains, particularly in the context of global green and low-carbon development. The findings reveal that digital transformation significantly reduces carbon emission intensity by 9.97% in upstream enterprises and 11.9% in downstream enterprises, highlighting the substantial spillover effects across the industrial chain. These reductions are driven by three mechanisms: innovation integration, information spillover, and resource allocation. The study also finds that these spillover effects are more pronounced in regions with lower economic growth targets and stricter environmental regulations, particularly in central-eastern China. Additionally, the research identifies significant industry heterogeneity, with varying spillover effects across different industrial sectors. This research offers valuable policy insights for leveraging digital transformation to promote green and low-carbon industrial transformations, especially in developing countries.

Emergency material reserve and dispatching are important measures to reduce casualties and property losses after natural disasters occur. However, there has not yet been research that optimizes both the reserve and distribution of emergency materials together. This paper investigates the joint optimization of reserve and dispatching for multivariety emergency materials. Considering the timeliness, economy, and safety of emergency rescue, a multiobjective joint optimization model for emergency material reserve and dispatching has been established, with the targets of minimizing the total delay time, minimizing the total cost, and maximizing the number of safely delivered. Given the uncertainty in the emergency rescue, this paper uses interval numbers to represent transportation speed and triangular fuzzy numbers to represent transportation costs. Then, we study the model solution method, which mainly includes the conversion of uncertain constraints and the NSGA-II algorithm used for calculating the proposed multiobjective model. In the end, a numerical example is provided to demonstrate the validity and effectiveness of the proposed model and solution method. The results of the comparative analysis indicate that the comprehensive weighting strategy proposed in this paper is more balanced than the strategy that uses a single objective value as the optimization objective.

Green finance is of vital significance for global rural sustainable development. This paper aims to explore the impact of green finance on rural sustainable development. Based on panel data obtained from 283 prefecture-level cities in China over the period from 2004 to 2022, a rural sustainable development indicator system was constructed under the DPSIR framework. By employing a fixed-effects model, moderation effect analysis, and the spatial Durbin model, a role for green finance in rural sustainable development and its spatial effects is proposed. The results of these analyses reveal the following: (1) Rural sustainable development exhibits a cyclical expansion–contraction trend; (2) green finance promotes rural sustainability, confirmed by robustness checks; (3) environmental regulations and the digital economy play a positive moderating role in enhancing the impact of green finance on rural sustainable development; (4) in terms of spatial effects, green finance has a positive effect within the region but can exert a negative spillover effect on surrounding regions. Based on these findings, it is proposed that the layout of green finance should be strengthened, environmental supervision should be enhanced, and the digital economy should be promoted. Such recommendations represent critical measures which can serve as the foundation to stimulate rural sustainable development and provide valuable references for relevant policy formulation.

Grain yield is affected by a variety of complex factors, with large volatility and randomness. In order to improve the accuracy of grain yield prediction, this paper proposes a grain yield prediction method with improved unbiased grey Markov model. In the unbiased grey Markov model, after the average division of states is performed, the values within each state are nonlinear. This paper proposes to replace the method of taking the median of the first and last transitions in the unbiased Markov chain with the average for the calculation of state division and to correct the residual values of the prediction results by using the improved unbiased grey Markov model, in order to improve the accuracy of the predicted value of grain yield. Simulation experiments were conducted to compare the grey GM (1, 1) model, the unbiased grey GM (1, 1) model, the unbiased grey Markov model and the improved unbiased grey Markov model. The original grain output data for Chongqing from 2000 to 2022 were used for the validation analysis to compare the prediction accuracies of the four models. The results show that the prediction accuracy of the grey GM (1, 1) model and the unbiased grey GM (1, 1) model is basically the same, with an average error of 3.213%. The prediction accuracy of the unbiased grey Markov model is better, with an average error of 2.039%. The unbiased grey Markov model has the smallest prediction average error of 1.367%. Compared with the previous three models, the improved unbiased grey Markov model can further improve the prediction accuracy, which is suitable for medium- and long-term prediction and predicts the grain production data of Chongqing in the next eight years.

The main objective of this study is to develop a fuzzy-based approach for building a multistage, multiproduct, and multiperiod supply chain network (SCN) after and before the COVID-19 pandemic. The proposed model optimizes production and distribution planning under uncertainty in a multiperiod stochastic process network. The model is designed to help decision-makers manage the green supply chain (GSC) of their organizations. It was developed using the mixed-integer linear programming (MILP) approach. The model aims to maximize customer satisfaction in the pre- and post-COVID-19 era by reducing the total cost and delivery time they face. The model also estimates production, asset locations, order allocation, and inventory levels. Under uncertain conditions, a new probabilistic MILP model addresses the multiproduct, multiperiod SCN design (SCND) problem. The two objectives of this model are to maximize time and cost by using the concepts of total cost of ownership, activity-based costing, and just-in-time (JIT) production. The model’s outputs include the quantity of goods purchased, produced, inventoried, delivered, and transported and the selection of suppliers before and after the COVID situation. A numerical example solved using the above technique is given to evaluate and validate the model and the proposed solution approach. Finally, the results of the study are presented.

We propose an envy-free team project called “color team project”. The primary motivation behind this approach is to prevent free-rider behavior and create a fair evaluation system that avoids jealousy among team members. In the team project, each team member indicates their contribution to the final team output using a color or their name. To evaluate the color team project, we use the number of pixels as the decision matrix, which includes pixels from the entire work (“All”), the methodology section (“Methodology”), the experimental section (“Results”), and the “Title”. The attribute weight is determined through steps that include standardization and information entropy. We then determine the ranking order of a team project using either the Simple Additive Weighting (SAW) method or the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method, and it is verified by the analytic hierarchy process (AHP) method. By applying the color team project, we can overcome the free-rider problem and maintain the positive aspects of team projects, such as effective communication, collaboration, and negotiation.

In this paper, an adaptive control strategy is developed for discrete-time switched nonlinear systems with actuator faults and dead-zone input under arbitrary switching conditions. The actuator faults considered include loss-of-effectiveness and bias faults, which are unknown but bounded. The complex structure of these systems, combined with actuator faults and dead-zone inputs, presents significant challenges for control and this problem is addressed by approximating the unknown functions of each subsystem using radial basis function neural networks. Under arbitrary switching signals, the suggested controller and adaptive laws ensure that all signals remain bounded and the system output tracks the reference signal with a small bounded tracking error. The efficiency of the control technique is proven by two numerical examples.

The main goal of this paper is to study blow-up of solutions of a weakly coupled system for semilinear wave equations with damping terms and mass terms in the de Sitter spacetime. The exponential, polynomial, and logarithmic growth of time-dependent factors in nonlinear terms are investigated by using iterative methods, respectively. Upper bound lifespan estimates of solutions to the problem are established. To the best of our knowledge, the results in Theorems 1.1–1.3 are new. In particular, the critical curve for exponents p,q in nonlinear terms in this problem is same as the critical curve for a weakly coupled system of semilinear wave equations with power nonlinearities. In addition, wave trends are expressed by numerical simulation.

In traditional production function research related to agricultural production, regional differences in agricultural labor capacity and information distribution are ignored. In the context of the digital economy (DE), this paper reintroduces information data as a new production factor to analyze the factor allocation mechanism. Based on previous studies, it conducts spatial Durbin model (SDM) analysis at the inter-provincial regional scale. It further studies the regional heterogeneity of land circulation distribution in China’s east, middle, and west. It finds that land circulation is consistent with the theory of the siphoning effect. DE (DE) variables accelerate the circulation of information factors and improve the allocative efficiency of land, technology, and capital factors. Finally, the article proposes suggestions on the role of the DE in improving agricultural production efficiency and narrowing the urban–rural gap.

In this note, the stability of neutral delay reaction–diffusion systems (NDRDS) was concerned by applying the matrix pencil and the Kronecker product. A new computing method for the distribution of imaginary axis eigenvalues on general n-dimensional NDRDS will be introduced. A practical, checkable criterion for the asymptotic stability will be derived. The main contribution of this paper is that we provide a computational method for determining imaginary axis eigenvalues and minimal delay margin on general NDRDS.

The generation and application of new self-media provide new ways to acquire information access for Internet users. It also provides a large amount of quality data for the accurate prediction of the Shanghai composite index. In this paper, we combined various machine learning and deep learning models with the search data of Chinese TikTok, which is related to the Shanghai composite index, to predict the Shanghai composite index. In addition, we compared and analyzed the prediction results of several machine learning and deep learning models in the short term, medium term, and long term. The results showed that the support vector regression model had the lowest mean absolute percentage error and the highest prediction accuracy in the short, medium, and long term, and the strongest robustness compared with other models. This was followed by random forest regression, which outperformed the remaining five benchmark prediction models (convolutional neural network, LSTM, GRU neural network, radial basis function neural network, extreme learning machine, and transformer model) in terms of prediction accuracy and robustness. The prediction results provide an innovative exploration of the prediction of the Shanghai composite index using self-media network search data. The prediction method provides a new research idea for macroeconomic prediction and forecasting and also enriches the theoretical research of machine learning methods in the field of macroeconomic index prediction.

A triopoly game is introduced to study the competition among three firms in a single market, each operating in an oligopolistic market. Our study is concerned with a static model in which the market has taxes and a quadratic cost function in quantity. In the static system we employ, known as Cournot-Bertrand, one firm’s output depends on quantity, while the other firms’ outputs depend on price. In the first part of this paper, we study the existence of the Nash equilibrium and its condition of stability for the static mixed model. In the second part of this paper, we modify the standard bounded rationality to fractional bounded rationality of discrete dynamical systems that have increasing taxes according to quantities based on the Egyptian market. Finally, we present a numerical study of the dynamical system, demonstrating that a small degree of memory enhances system stability.

This study develops a stochastic optimal control model to optimize dynamic pricing and production strategies for fashion retailers facing uncertain demand and rapid product devaluation. Applying the Hamilton–Jacobi–Bellman equation approach, we derive profit-maximizing joint pricing and production policies. Key findings include the following: (1) Dynamic pricing and responsive production strategies outperform static pricing in terms of expected discounted profit under various market conditions. (2) Optimal dynamic prices exhibit a declining trend over the product lifecycle, aligning with observed practices in fast fashion. (3) The optimal production rate adapts to current inventory levels and market conditions, balancing the trade-off between stockouts and holding costs. (4) The model demonstrates robustness to variations in price elasticity, providing a flexible decision framework for diverse fashion market segments. (5) Extreme demand volatility reduces the economic benefits of dynamic policies, highlighting the need for additional risk management strategies. This research contributes to sustainable operations’ literature by integrating pricing and production decisions under uncertainty, offering theoretically grounded and practical insights for fashion retailers to enhance profitability and reduce waste.

Based on Chinese industrial enterprises data and Chinese customs data from 2000 to 2013, the paper examines the micromechanism of intellectual property rights protection affecting the quality upgrade of firms’ export products. The empirical results show that strengthening intellectual property right (IPR) protection has a specific and significant role in promoting the quality upgrade of firms’ export products; the estimation results are still robust after using instrumental variables to overcome endogenous biases. Heterogeneity analyze results show that IPR protection has a relatively more significant effect on the quality improvement of export products for foreign-funded firms, high-tech industry firms, firms that import intermediate goods from OECD countries, and firms that import high-tech intermediate goods. Further analysis finds that IPR protection promotes quality upgrade of firms’ export products through the intermediate goods quality effect, product category effect, and technology spillover effect; the expansion of the scale of imported intermediate products brought about by the strengthening of IPR protection has produced a “substitution effect” on the production capacity and R&D capabilities of Chinese upstream industries, and when expanding production capacity, it is necessary to strengthen technology research and development capabilities of the upstream intermediate product industry and improve the quality and technology of intermediate products so as to alleviate the negative impact of the expansion of foreign intermediate product imports and supply. Strengthening IPR protection will further enhance the “Washington apple effect” of the import of intermediate goods, and special attention should be paid to import partners with the long-distance and high-quality intermediates in the formulation and implementation of trade policies. The study is helpful for policymakers to formulate correct and effective IPR protection policies and foreign trade policies and also provides empirical evidence and useful inspiration for improving Chinese enterprises’ innovation level and promoting the upgrading of intermediate products production under the current IPR protection strategy.

The prevalence of B2B platform ecosystem has led to the emergence of revenue-sharing contracts as the dominant business model adopted by manufacturers and retailers on these platforms. This paper establishes a dynamic game model of B2B platform ecosystem, comprising one manufacturer and one retailer, where the manufacturer engages in technological investments and the retailer engages in consumption investments, both exhibiting bounded rationality. Through a comprehensive analysis of complex behaviors, the results reveal the following: (1) Adjustment speed of the manufacturer influences the stability of the platform ecosystem, with higher adjustment speeds leading to greater instability. In a stable state of the B2B platform ecosystem, an actor with lower costs tends to make higher investments. (2) Higher investment costs contribute to a more stable B2B platform ecosystem. When the ecosystem stabilizes, increasing investment costs will reduce manufacturers’ investment levels. (3) The retailer revenue sharing parameter exacerbates the instability of the B2B platform ecosystem. This unequal distribution not only impairs manufacturers’ earnings but also disrupts B2B platform ecosystem equilibrium. (4) Market expansion results in B2B platform ecosystem imbalance. As the market size increases, investment levels rise, but this also leads to system instability. Therefore, managers must strike a balance between market expansion and system stability objectives. (5) We incorporate the time-delayed feedback control (TDFC) method to regulate intricate phenomena. The TDFC method proves effective in mitigating chaotic behaviors within B2B platform ecosystem.

This article assesses the hedging and safe haven properties of energy and agricultural commodities (crude oil, natural gas, and wheat) against the G7 stock market indices and banking sector stock indices during the COVID-19 pandemic, the Russia–Ukraine military conflict, and the Silicon Valley Bank (SVB) collapse. Using wavelet coherence analysis, our results showed dynamic correlations in which commodities shifted from diversifiers to strong safe havens during periods of turmoil. Particularly, WTI became a safe haven during the SVB collapse, natural gas acted primarily as a safe haven during the pandemic, and wheat evolved into a robust safe haven during crises. Moreover, our results with the G7 banking sector stock indices underscore the safe haven ability of commodities against these financial assets, furnishing valuable insights for investors during unstable financial situations.

Cholera is a global threat to public health and is an indicator of inequity and lack of social development. By the World Health Organization (WHO), there are 1.3–4.0 million cases of cholera and 21,000–143,000 deaths worldwide due to the infection each year. This innovative work discusses the spread of the cholera virus; the model of this disease was formulated mathematically and solved with the help of the artificial neural network technique. The developed model identified the nonlinear ordinary differential equations represented by susceptible (Sc), vaccinated (Vc), infectious (Ic), recovery (Rc), and concentration of cholera in water (Bc) and the cholera model reference dataset is formed using the explicit Runge–Kutta method. A dataset is arbitrarily used for each cyclic update in Levenberg–Marquardt backpropagation for the numerical study of cholera dynamics. The Levenberg–Marquardt backpropagation is implemented to refine the dataset of the cholera model for training, testing, and validation. The accuracy of the proposed technique is evaluated through mean squared error (MSE), error histograms, merit functions, reliable performance, and regression. These findings underscore the potential of intelligent optimization to enhance the precision of epidemic predictions and inform more effective, targeted cholera control strategies. Thus, intelligent optimization offers a valuable tool for public health response in vulnerable areas.

The advent of social media (SM) platforms has transformed communications, information dissemination, and interpersonal relationships on a global scale. As SM continues to evolve and proliferate, its impact on various aspects of society has become increasingly complex and multifaceted. For this reason and over the past decades, several controversies have been held about whether SM is good or bad. However, the mathematical modeling technique inculcating SM impacts (positive and negative) has not been studied in the existing works. This article considers a mathematical model approach using the ABC-fractional derivative technique to study the dynamics of SM impacts. We provide the various definitions and the properties needed to study the model. Also, we use the fixed point theorem and a nonlinear analytic approach to demonstrate the theoretical solutions of the existence of solutions for the proposed model. Furthermore, the fundamental reproduction number is computed, and the stability of the model is achieved using the Ulam–Hyers (HU) criteria. We again perform a sensitivity study for the SM impact model and the effects of the sensitive parameters are presented in 3D and contour plots. In addition, a numerical algorithm of the predictor–corrector type of the Adams–Bashforth method for determining the approximate solution of the model is developed and the results are discussed. The effects of the most sensitive parameters on affected individuals in the model with a constant fractional order are shown and discussed. The simulation results indicate that as individuals become aware of the negative impacts of SM, the number of positively impacted individuals rises.

This study investigates what determines social media consumption in private and public locals. Based on a survey of 638 citizens, we found that the daily consumption frequency of social networks, and face-to-face, both inversely influence consumption in private places, the daily consumption frequency of the Internet inversely influences consumption in both private and public places, and daily consumption frequency of mobile phones inversely influences consumption in the private place. Results conclude that daily consumption frequency of the Internet mediates the effect of time spent on the Internet, watching and listening in private local; daily consumption frequency of mobile phones mediates the effect of time spent on the Internet, reading, watching and listening in private local. We also found that daily consumption frequency of the Internet mediates the effect of time spent on the Internet, reading and listening in public local, and daily consumption frequency of social networks mediates the effect of time spent on the Internet, reading, watching and listening in public local.