Collective Behavior Of Complex Network Systems

In nature,wolves,birds,fishes,and others often exhibit complex collective behaviors.From a mathematical point of view,these groups of organisms can be considered as complex systems.The collective behavior of complex systems has been widely concerned by scholars.Complex networks and multi-agent systems are two important branches of complex systems.However,previous studies have often neglected the influence of long-range interactions between individuals or specific network structures on collective behavior.In this paper,we discuss the finite-time consensus problem of multi-agent systems with long-range interactions,the opinion consensus control problem of multiplex networks,and the synchronization problem of multiplex networks with random topologies.The main research of this paper is as follows:First,the finite-time consensus problem and finite-time stochastic consensus problem of multi-agent systems with long-range interactions are studied.Taking into account the indirect interactions between agents,a long-range interaction control protocol is designed by combining the finite-time control technology.The estimation of the upper bounds on the time and energy cost of the multi-agent systems achieve consensus are given by using the stability theory of differential equations and matrix analysis and compared with the traditional finite-time control protocol.The effects of control parameters and network size on the convergence time and energy cost of the multi-agent systems are analyzed by numerical simulations.Second,the opinion consensus control problem of multiplex networks is investigated.An opinion dynamics model of multiplex networks consisting of Internet-real society is developed which combines three mechanisms of bounded confidence,interaction topologies,and Internet-real society interactions.By introducing virtual agents satisfying certain rules in the Internet layer,the sufficient condition for the system to achieve consensus of the target opinion values is obtained.And the case that virtual agents only guide some real agents is considered.In the numerical simulation,the effects of different control strategies and target opinions on the convergence process are compared.Finally,the synchronization problem of multiplex networks with random topologies is studied.A nonlinear multiplex network model with random topologies is developed,and the number of layers of the system can be arbitrary.Considering the effect of layer similarity on network synchronization,a general framework for analyzing the synchronization of multiplex networks with layer similarity is proposed.Using random matrix theory,sufficient conditions for the synchronization of multiplex networks with strong and weak inter-layer coupling are obtained,respectively,and the main factors affecting the synchronization of multiplex networks are analyzed.The correctness of the theoretical results was verified by numerical simulations.