Asymptotic Flocking Analysis For Generalized Cucker-Smale Models With Processing Delays

Collective behavior is a ubiquitous phenomenon in nature,such as bird migration,fish foraging and bacterial m ovement.Through simple rules,a large number of agents can evolve from a disordered state into ordered collective behavior.In recent years,the study of collective behavior of multi-agent systems has attracted much attention of many scholars,especially the hot topics of the relevant mathematical model,flocking dynamics,cluster control,et al.In this paper,several kinds of generalized Cucker-Smale models are studied,sufficient conditions for the existence of asymptotic flocking solutions are given,the effects of piecewise interaction functions and processing delays on the asymptotic flocking behavior are studied,and the flocking dynamics with strategies are described.The main contents include:Firstly,for the generalized Cucker-Smale model with piecewise interaction functions,on the one hand,an initial condition for maintaining the topological structure of the system is given by matrix analysis and graph theory,and then sufficient conditions for the system to achieve asymptotic flocking are o btained.On the other hand,the critical value of the delay parameter is obtained by the operator theory of functional differential equations and inequality estimation.When the parameter is within the critical threshold,the system would achieve asymptotic flocking.Secondly,for the generalized Cucker-Smale model with strategies,sufficient conditions for flocking and bi-flocking are given respectively by the Lyapunov function method,and the effects of strategies on asymptotic flocking are di scussed.In addition,the influence of time-delay on the asymptotic behavior of the system is analyzed by the flocking theory of time-delay Cucker-Smale model and the qualitative theory of functional differential equation,and the critical threshold estimation of the time-delay parameter is obtained.When the parameter is within the critical threshold,the system would achieve asymptotic flocking.