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

作　　者：徐伟[1] 贺群[1] 戎海武 方同[3] 

机构地区：[1]西北工业大学应用数学系,西安710072 [2]佛山科技学院应用数学系,佛山528000 [3]西北工业大学振动工程研究所,西安710072

出　　处：《物理学报》2003年第6期1365-1371,共7页Acta Physica Sinica

基　　金：国家自然科学基金 (批准号 :10 0 72 0 49)资助的课题~~

摘　　要：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.

关 键 词：随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍 Duffing-van-der-Pol振子 拓扑性质 

分 类 号：O322[理学—一般力学与力学基础]