Duffing-van der Pol振子随机分岔的全局分析

Global analysis of stochastic bifurcation in a Duffing-van der Pol system

应用广义胞映射方法研究了参激和外激共同作用的Duffing vanderPol振子的随机分岔 .以系统参数通过某一临界值时 ,如果系统的随机吸引子或随机鞍的形态发生突然变化 ,则认为系统发生随机分岔为定义 ,分析了参激强度和外激强度的变化对于随机分岔的影响 .揭示了随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的 .分析表明 ,广义胞映射方法是分析随机分岔的有力工具 。

Stochastic bifurcation of the Duffing-van der Pol oscillators under both additive and multiplicative random excitations is studied in detail by the generalized cell mapping method using digraph.As an alternative definition,stochastic bifurcation may be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value.It is found that under certain conditions stochastic bifurcation mostly occurs when a stochastic attractor collides with a stochastic saddle.Our study reveals that the generalized cell mapping method with digraph is also a powerful tool for global analysis of stochastic bifurcation.By this global analysis ,the mechanism of development,occurrence,and evolution of a stochastic bifurcation can be explored clearly and vividly.