双时滞van der Pol方程的数值Hopf分支

Analysis of numerical Hopf bifurcation for van der Pol equation with double time delays

研究Runge-Kutta方法对以时滞为参数的双时滞van der Pol方程的数值Hopf分支问题。证明当该方程分支参数值在τ1=τ01处产生Hopf分支时,其数值解相应地在分支参数值τ1*=τ01+O(hp)处产生Hopf分支(p为Runge-Kutta方法的方法阶),且以解析解的分支参数值为极限,从而论证了双时滞van der Pol方程数值解保持其原解析解的动力学特性。

Numerical Hopf bifurcation of van der Pol equation with parametric double time delays is studied by using the method of Runge-Kutta. It is proved that, when analytic solution undergoes a Hopf bifurcation at rl = ~＇~1, the numerical solution correspondingly undergoes a Hopf bifurcation at T1＊ = T^O1 ＋ 0 （h^p） （p is the method order of Runge-Kutta） , and more ,the bifurcate point of analytic solution is absolute the limited point of the numerical one＇ s. Therefore, the numerical solution of van der Pol equation with double time delays maintains the dynamics characteristics of its original analytic solution under the method of Runge-Kutta.