强迫Duffing—Van der Pol振子的混沌行为

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.     

Biological applications of the “Filtered” Van der Pol oscillator

The present article deals with the development of an oscillatory model, which generates waveforms corresponding to ECG patterns. The present oscillatory system relies on coupling of oscillators derived from the famous VDP oscillator. We demonstrate that inducing a relaxation type of dynamics in the models contributes to their successful generation of ECG like signals. Furthermore, an interesting affinity is found, which associates the present models with a version of the well-known practical Wien Bridge oscillator. The presently discussed system relies on coupled elementary oscillator units. The present coupling is due to merely two units. The model, however, is likely to become even more realistic by coupling in the same manner an assembly of relatively many oscillators.