The psychology of the individual is continuously changing in nature, which has a significant influence on the evolutionary dynamics of populations. To study the influence of the continuously changing psychology of individuals on the behavior of populations, in this article, we consider the game transitions of individuals in evolutionary processes to capture the changing psychology of individuals in reality, where the game that individuals will play shifts as time progresses and is related to the transition rates between different games. Besides, the individual’s reputation is taken into account and utilized to choose a suitable neighbor for the strategy updating of the individual. Within this model, we investigate the statistical number of individuals staying in different game states and the expected number fits well with our theoretical results. Furthermore, we explore the impact of transition rates between different game states, payoff parameters, the reputation mechanism, and different time scales of strategy updates on cooperative behavior, and our findings demonstrate that both the transition rates and reputation mechanism have a remarkable influence on the evolution of cooperation. Additionally, we examine the relationship between network size and cooperation frequency, providing valuable insights into the robustness of the model.

Epidemic spreading processes on dynamic multiplex networks provide a more accurate description of natural spreading processes than those on single layered networks. To describe the influence of different individuals in the awareness layer on epidemic spreading, we propose a two-layer network-based epidemic spreading model, including some individuals who neglect the epidemic, and we explore how individuals with different properties in the awareness layer will affect the spread of epidemics. The two-layer network model is divided into an information transmission layer and a disease spreading layer. Each node in the layer represents an individual with different connections in different layers. Individuals with awareness will be infected with a lower probability compared to unaware individuals, which corresponds to the various epidemic prevention measures in real life. We adopt the micro-Markov chain approach to analytically derive the threshold for the proposed epidemic model, which demonstrates that the awareness layer affects the threshold of disease spreading. We then explore how individuals with different properties would affect the disease spreading process through extensive Monte Carlo numerical simulations. We find that individuals with high centrality in the awareness layer would significantly inhibit the transmission of infectious diseases. Additionally, we propose conjectures and explanations for the approximately linear effect of individuals with low centrality in the awareness layer on the number of infected individuals.

Dynamic processes in complex network are crucial for better understanding collective behavior in human societies, biological systems, and the Internet. In this article, we first focus on the continuous Markov-based modeling of evolving networks with the birth-death of individuals. A new individual arrives at the group by the Poisson process, while new links are established in the network through either uniform connection or preferential attachment. Moreover, an existing individual has a limited lifespan before leaving the network. We determine stationary topological properties of these networks, including their size and mean degree. To address the effect of the birth-death evolution, we further study the information dynamics in the proposed network model from the random drift and natural selection perspective, based on assumptions of total-stochastic and fitness-driven evolution, respectively. In simulations, we analyze the fixation probability of individual information and find that means of new connections affect the random drift process but do not affect the natural selection process.

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this article, we introduce a complex network model that considers the stochastic switching of individuals between activated and quiescent states at power-law rates and the corresponding evolutionary dynamics. By using the Markov chain and renewal theory, we discover a homogeneous stationary distribution of activated sizes in the network with power-law activating patterns and infer some statistical characteristics. To better understand the effect of power-law activating patterns, we study the two-person-two-strategy evolutionary game dynamics, demonstrate the absorbability of strategies, and obtain the critical cooperation conditions for prisoner’s dilemmas in homogeneous networks without mutation. The evolutionary dynamics in real networks are also discussed. Our results provide a new perspective to analyze and understand social physics in time-evolving network systems.

With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated.