三稳态Van der Pol系统随机P分岔电路实验研究

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (13) : 111-116.

论文

吴志强，王文博，张祥云

作者信息 +

A tri-stable Van der Pol system’s stochastic P-bifurcation circuit experiment

WU Zhi-qiang WANG Wen-bo ZHANG Xiang-yun

Author information +

文章历史 +

摘要

设计了高斯白噪声激励下的三稳态Van der Pol电路随机动力学实验系统，并从响应的时间历程图、相图、稳态概率密度图三方面，实验研究了高斯白噪声强度变化对系统三稳态切换行为的影响。结果表明，随着激励强度增加，不同吸引子间的切换频率显著改变,并且概率密度曲线上的峰之间相对高低发生变化，实验数据点在相图上的分布逐渐趋于均衡化，概率密度曲线峰的数目发生变化，通过与理论结果对比，定性验证了随机P分岔现象的发生。

Abstract

A Van der Pol circuit system with one stable equilibrium point and two stable limit cycles under the excitation of Gaussian white noise was designed for stochastic dynamics experiment. The effects of Gaussian white noise intensity change on the switching behavior among three steady states of the system was experimentally studied from three aspects including response amplitude time history diagram, phase diagram, and steady state probability density diagram. The results shown that with increase in excitation intensity, the switching frequency among different attractors varies significantly; the relative height between peaks and the peak number of the probability density curve change; Moreover, the distribution of experiment data points in the phase diagram gradually tends to equalization; compared with the theoretical results, the occurrence of the stochastic P-bifurcation phenomenon was qualitatively verified.

导出引用

吴志强，王文博，张祥云 . 三稳态Van der Pol系统随机P分岔电路实验研究[J]. 振动与冲击, 2018, 37(13): 111-116

WU Zhi-qiang WANG Wen-bo ZHANG Xiang-yun. A tri-stable Van der Pol system’s stochastic P-bifurcation circuit experiment[J]. Journal of Vibration and Shock, 2018, 37(13): 111-116

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