一类具有时滞负反馈项的离散型网络拥塞模型的稳定性分析

Stability analysis of a class of discrete network congestion model with delay negative feedback terms

研究了一类加入负反馈项的时滞离散型网络拥塞模型.首先给出了正不动点渐近稳定的条件,其次以时滞作为参数,给出了产生Neimark-Sacker分支的延迟临界值序列,最后,利用Hassard的思想,分析了分支方向和周期解稳定性,并采用数值模拟验证了所得结果的正确性.

In this paper, a delay discrete network congestion model with negative feedback term was studied. Firstly, the conditions of stability of positive fixed point were given. Choosing the time delay as a parameter, we obtained a sequence critical value of Neimark-Sacker bifurcation occurring. By Hassard’s idea, the direction of bifurcation and the stability of periodic solutions were analysed. Simulation results had been verified and demonstrated the correctness of the theoretical results.