无线网络拥塞控制中流体流模型的Hopf分岔及其稳定性

该文对一个用于无线网络拥塞控制算法设计的具有通信时延的流体流模型进行Hopf分岔分析，以通信时延作为分岔参数，证明此模型Hopf分岔的存在性，并应用中心流形和规范型理论推导出确定 Hopf 分岔方向和分岔周期解稳定性的计算公式，数值仿真验证了结论的有效性。

Stability and Hopf Bifurcation of a Fluid-Flow Model for Congestion Control in Wireless Networks

This paper focuses on the Hopf bifurcation analysis of a fluid-flow model with time-delay for the congestion control algorithm in the wireless networks. By choosing the communication delay as a bifurcation parameter, the model exhibits of Hopf bifurcation are proved. The formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, a numerical simulation is presented to verify the theoretical results.