受时滞影响的双个体自组织系统的集群性

Flocking in A Two-Agent System with Processing Delay

研究了受Motsch-Tadmor影响函数控制和处理时间延迟影响的双个体Cucker-Smale自组织模型,将现有的充分性结果进行了推广,给出了双个体自组织系统产生集群行为的充分必要条件,同时也揭示了时滞的大小对系统集群性的影响.数值模拟验证了结果,并表明在固定初始条件和参数的情况下,时滞的变化会导致系统出现集群行为,集群行为消失,周期振荡等分支现象.

Based on Cucker-Smale model and Motsch-Tadmor＇s influence function,the necessary and sufficient conditions for a two-agent model with processing delay to induce time-asymptotic flocking are provided.The magnitude of processing delay can affect the flocking of the model which is proved in the simulation results.It is also shown that in an occasion of fixing initial conditions and parameters,changing processing delay will result in various bifurcation phenomena including flocking,none-flocking and periodical oscillatory.