受周期扰动的Van der Pol方程振荡解的数值模拟

A Numerical Analogue of the Oscillation Solution for Van der Pol Equation Subjected to Period Disturbance

对著名的VanderPol方程受周期扰动的振荡解进行了一系列的数值模拟．由其数值模拟结果可知，VanderPol方程在零阶项受到正弦周期扰动时，其形如x－（1－x2）x十xμsint＝0，当可调参数μ在［0.1，1］之间，本方程均表现出强非线性性质．在未受到扰动时，它存在极限环，即一个简单的吸引子，而受到扰动时极限坏消失了，出现了一个具有对称小圆环的奇怪吸引子．从其相平面的混沌吸引子及其流的分析可知，由于有了此项扰动，本动力系统呈现出阵发性的拟周期的混沌振荡运动．如果将方程中的sint换成cost其模拟结果基本一样．

A series of numerical analogue to oscillation solufion of Van der Pol equation which is disfurbed periodically has realized. From the numerical amalogue results,Van der Pol equation is describld as x - (1 -x2)x+xμ sin t= 0 while its zero order term is subjected to sinusoidal periodical disfurbance. And it expresses strong non-linearity when its adjustable parameter μ is in[0' 1' 1]. When it is not supjected to disturbance,it has a limit-cycle,which is a simple attractor,while it is subjected,the limit-cycle disappered and a strange attracfor with a small symmetric cycle occures. It is clear that,from the analysis of the phase plane chaotic attractor and its flow,this dynamic system expresses as chaotic oscillation motion 'with intermittent quasi-period because of the disturbance. If the sint is substituted for cost,the simulation result will be the same.