Research On Dynamics And Controllability Of Evolutionary Game Based On Multi-layer Complex Network

Evolutionary game theory is a theory produced by the combination of biological evolution theory and classical game theory.It provides an effective analysis framework for the evolution of individual strategies in the population.With the deepening of the research on evolutionary game,the hierarchical and complex system model has gradually increased.Based on the research results of interdependent networks in complex networks,this paper studies the problems of evolutionary game dynamics,cooperation emergence,and controllability of binary Boolean networks by constructing a multi-level network model.The main tasks are as follows:(1)Based on the interdependent networks,the memory factor is introduced into the prisoner game model.This paper studies the influence of memory effect and the strength of association between interdependent networks on the dynamics of system game and discusses the evolution law of cooperative behavior among players with memory ability.Then,divide the participants who in the system into four types and analyse the distribution characteristics of different types of participants who keep a stable state in the system.(2)Under the interdependent networks model,we study the dynamic evolution process of the third strategy prisoner game.In order to describe the behavior of risk aversives in reality,we add the neutral strategy into the system as the third strategy,so the game model is extended from binary to three-valued strategy and we discuss the evolutionary game behavior of participants.On the basis of discussing the influence of the interdependent networks structure on the dynamics of the three-valued strategy game model,the global strategy oscillation phenomenon that emerged in the evolutionary game is studied using phase diagrams,Lypunov exponents,and other analysis tools.The characteristics of chaos were studied.(3)Considering the interdependent strength between interdependent networks as a limited resource,we study the co-evolutionary of interdependent strength and game strategy.In the interdependent networks architecture,the behaviors of the game groups will influence each other,and the coupling forces among the networks will be regarded as free distribution resources.The self-organizational behavior of the group evolution game will be studied.Based on the analysis of the distribution characteristics of the correlation strength at steady state,we make a discussion about co-evolutionary dynamic behavior and the emerging phenomenon of cooperation.(4)Based on Harvey asynchronous update method,the controllability of Boolean networks with external input control is studied.The matrix semi-tensor product technique is used to linearize the binary Boolean logic system to obtain a universal control-based network transition matrix.Further,three control methods,ie,free control sequence,input control network and closed-loop control,are used to discuss the controllability of asynchronous Boolean networks,The conditions determining the controllable states and the construction methods for their control sequences are given.