一类延迟微分方程Rosenbrock方法的数值Hopf分支

Numerical Hopf bifurcation of Rosenbrock methods for a Class of Delay Differential Equations

本文应用Rosenbrock方法将一类d维的含参数的延迟微分系统离散化,得到相应的数值离散系统。证明了如果原系统存在Hopf分支,则相应的数值离散系统Hopf分支的分支方向和不变曲线的稳定性分别与原系统的分支方向和周期解的稳定性相同。并由数值试验进一步验证了理论分析的结论。

A class of delay differential equations with parameter is considered. Applying the Rosenbrock methods to the system,the corresponding numerical discrete system is obtained. It is proved that if the original system undergoes a Hopf bifurcation,the direction and the stability of the invariant curve of the numerical discrete system are the same as that of the original syetem. Numerical experiment further confirms the theoretical results of numerical analysis.