强迫Duffing-Van der Pol振子的混沌行为

Chaotic Behaviours of Forced Duffing-Van der Pol Oscillator

用Melnikov-Holmes方法对如下强迫Duffing-Van der Pol振子进行了分析:给出其同宿轨道的Melnikov函数及系统产生混沌的阈值.通过数值计算,运用运动轨线的直接观察,相图分析和FFT功率谱分析方法,考察系统的周期和混沌行为.并着重研究了反馈周期驱动对系统混沌行为的影响.在小参数范围内,数值结果与理论结果符合较好.本文的研究结果将为解决非线性系统的噪声干扰问题以及获得在统计分析和Monte Carlo方法中极为有用的具有给定分布的随机信号等提供途径.

The system of forced Duffing-Van der Pol Oscillator which is described as: is discussed by Melnikov-Holmes method. Melnikov function of homoclinic orbit and threshold of chaos are at- tained. We also examined the periodic and chaotic behaviours of the system with numerical method, there are time history observations, phase portraits, FFT power spectrum analysis. It is studied emphatically to the influ- ence of feedback periodic driving on the chaotic behaviours. This is in agreement with the theoretical conclusions in small parameter range. The numerical results will provide a way for nonlinear systems escaping from noisy in- terference and gain the stochastic signal plossessing certain distribution that used widly in statistic analysis and Monte Carlo method.