Discrete Dynamics in Nature and Society
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Acceptance rate26%
Submission to final decision52 days
Acceptance to publication33 days
CiteScore1.600
Impact Factor0.870
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Maximum Reciprocal Degree Resistance Distance Index of Unicyclic Graphs

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Discrete Dynamics in Nature and Society publishes research that links basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.

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Bifurcation and Chaos of a Discrete-Time Population Model

A Leslie population model for two generations is investigated by qualitative analysis and numerical simulation. For the different parameters a and b in the model, the dynamics of the system are studied, respectively. It shows many complex dynamic behavior, including several types of bifurcations leading to chaos, such as period-doubling bifurcations and Neimark–Sacker bifurcations. With the change of parameters, attractor crises and chaotic bands with periodic windows appear. The largest Lyapunov exponents are numerically computed and can verify the rationality of the theoretical analysis.

Research Article

Evolution Dynamics of Agricultural Internet of Things Technology Promotion and Adoption in China

Internet of Things is the core technology of smart agriculture and can reform and upgrade traditional agriculture for reducing cost, reducing pollution, and increasing productivity and quality in China. From government-led and market economy perspectives, promotion mechanisms and sustainable adoption of agricultural Internet of Things technology are analyzed. In the initial application phase, the promotion of Internet of Things requires government support. For investigating the relationship between the government and farmers, this study builds an evolutionary game model and finds that increases of cost subsidy, farmers’ negative feedback, government’s positive feedback, and chemical agriculture cost can make the model evolve toward the strategy set: farmer adoption and government support. For long-term development, a sustainable model in competitive market is built by competition game and exponential replication equation. This paper analyzes the equilibrium of adoption ratio, long-run profit, and the conversion between equilibrium points under capacity sharing strategy in competitive market. It is also found that the market will eventually evolve to the technology selection strategy whose long-run average profit dominates the market. The innovations are that evolutionary game is used for analyzing the initial stage and competitive game and asynchronous update mechanism are used for analyzing the sustainable development adoption. At last, references are provided for agricultural Internet of Things development policy from the perspectives of initial promotion and long-run sustainability.

Research Article

Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model

The aim of this paper is to study and investigate the optimal control strategy of a discrete mathematical model of drug consumption. The population that we are going to study is divided into six compartments: potential drug users, light drug users, heavy drug users, heavy drug users-dealers and providers, temporary quitters of drug consumption, and permanent quitters of drug consumption. Our objective is to find the best strategy to reduce the number of light drug users, heavy drug users, heavy drug users-dealers and providers, and temporary quitters of drug consumption. We use four control strategies which are awareness programs through media and education, preventing contact through security campaigns, treatment, and psychological support along with follow-up. Pontryagin’s maximum principle in discrete time is used to characterize the optimal controls. The numerical simulation is carried out using MATLAB. Consequently, the obtained results confirm the effectiveness of the optimization strategy.

Research Article

Stability, Neimark–Sacker Bifurcation, and Approximation of the Invariant Curve of Certain Homogeneous Second-Order Fractional Difference Equation

We investigate the local and global character of the unique equilibrium point and boundedness of the solutions of certain homogeneous fractional difference equation with quadratic terms. Also, we consider Neimark–Sacker bifurcations and give the asymptotic approximation of the invariant curve.

Research Article

C-SIW Rumor Propagation Model with Variable Propagation Rate and Perception Mechanism in Social Networks

The propagation of rumor has become a common phenomenon in social networks. Studying the dynamic propagation of rumor can help locate the key points to control rumor propagation. To further research the internal motivation of state transition, a corrector-ignorant-spreader-weakener (C-SIW) model is proposed in this paper. When the individual changes state to transmit rumor, the neighbor may have a significant impact on rumor propagation. Considering the point, this paper constructs a function to describe the propagation rate, which relates to the state of neighbors and the reputation of the spreader. In addition, perception from life also can cause individual state changes. Based on the above fact, the links from the spreader and the weakener to the corrector are added to describe the perception mechanism. Then, combining the derived average field equations, the steady state of the model is analyzed and verified in experimental simulation. Moreover, the experimental results on different networks show that the perception mechanism reduces the rumor influence. Besides, the variable propagation rate can position the fast-growing stage of rumor propagation more accurately and facilitate the control of rumor propagation.

Research Article

Lyapunov Stability Analysis of a Delayed Foot-and-Mouth Disease Model with Animal Vaccination

Foot-and-mouth disease virus remains one of the most important livestock diseases in sub-Saharan Africa and several Southeast Asian countries. Vaccination of livestock has been recognized as an important tool for the control of foot-and-mouth disease virus. However, this intervention strategy has some limitations. Generally, vaccine production is a complex multistep process which involves development, manufacturing, and delivery processes, and through this extensive process, some challenges such as poor vaccine storage often arise. More often, these challenges alter the validity of the vaccination. Foot-and-mouth disease virus epidemic dynamics have been extensively explored, but understanding the role of vaccination validity on virus endemicity is lacking. We present a time-delayed foot-and-mouth disease model that incorporates relevant biological and ecological factors, vaccination effects, and disease carriers. We determined the basic reproduction number and demonstrated that it is an important metric for persistence and extinction of the disease in the community. Numerical illustrations were utilised to support some of the analytical results.

Discrete Dynamics in Nature and Society
 Journal metrics
Acceptance rate26%
Submission to final decision52 days
Acceptance to publication33 days
CiteScore1.600
Impact Factor0.870
 Submit

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