分布式时延范台坡方程的Hopf分岔

详细信息

Hopf Bifurcation for Van Der Pol Equation with Distributed Delay

1.
School of Opto-Electronic Information,UEST of China Chengdu 610054;
2.
Department of Mathematics,Southwest University of Finance and Economics Chendu 610074;
3.
School of Electronic Engineering,UEST of China Chengdu 610054

摘要: 分析了分布式时延的范台坡方程,将平均时延作为分岔参数,证明了模型经历了Hopf分岔过程,用图示Hopf理论获得了判定分岔周期解的稳定性和分岔方向的准则。并应用数字仿真的例子证明了理论分析的正确性。
- 范台坡方程 /
- 分布时延 /
- Hopf分岔 /
- 周期解
Abstract: The van der Pol equation with a distributed time delay is analyzed. By using the mean time delay as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcations. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the graphical Hopf bifurcation theory. Numerical simulation examples for justifying the theoretical analysis are also given.
- van der Pol equation /
- distributed delay /
- Hopf bifurcation /
- periodic solutions