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本文利用数值模拟的方法研究了非线性Van der Pol系统在只受循环噪声随机力激励下的相干共振问题,通过研究循环噪声中的时滞对噪声型Van der Pol系统在临近Hopf分叉处输出信号的信噪比(SNR)、最频繁出现振幅以及功率谱密度等特性的影响来揭示系统在敏感范围内的动力学行为。有别于以往的只能通过单一的噪声强度来影响振子相干振动的方法。研究结果表明,利用噪声中的时滞也可以控制Van der Pol系统中噪声引起的振子的运动。
In this paper, the problem of coherent resonance of a nonlinear Van der Pol system excited by a random noise subjected only to circulating noise is investigated by means of numerical simulation. By studying the delay in the circulating noise, the output of a Van der Pol system with noise near the Hopf bifurcation Signal to noise ratio (SNR), the most frequently occurring amplitude and power spectral density and other characteristics of the system to reveal the system dynamics in the sensitive range. Different from the past, it can only influence the vibration of the oscillator by a single noise intensity. The results show that the noise-induced oscillator motion can also be controlled by using the time delay in noise.