Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise
Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise
复制标题
具有有色噪声的双稳态 Duffing-Van der Pol 振荡器中的随机分岔
DOI：
10.1103/physreve.83.056215
复制
发表时间：
2011-05-26
影响因子：
2.4
通讯作者：
Duan, Jinqiao
中科院分区：
文献类型：
--
作者：
Xu, Yong;Gu, Rencai;Duan, Jinqiao
研究了高斯色噪声诱导的Duffing-Van der Pol振子的随机分岔以及关联时间和噪声强度对分岔的动力学影响。利用随机平均方法，理论上可以得到Duffing-Van der Pol振子振幅的平稳概率密度函数，并揭示高斯色噪声影响下的有趣动力学行为。通过定性的变化的平稳概率分布，这表明系统参数，噪声强度，和噪声相关时间，分别讨论了随机分岔，可以被视为分岔参数。它们还意味着乘性噪声的影响与加性噪声的影响是相当不同的。直接数值模拟的结果验证了理论分析的有效性。最大李雅普诺夫指数计算表明，P分支和D分支之间没有直接联系.
This paper aims to investigate Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator. By using the stochastic averaging method, theoretically, one can obtain the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and can reveal interesting dynamics under the influence of Gaussian colored noise. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that system parameters, noise intensity, and noise correlation time, respectively, can be treated as bifurcation parameters. They also imply that the effects of multiplicative noise are rather different from that of additive noise. The results of direct numerical simulation verify the effectiveness of the theoretical analysis. Moreover, the largest Lyapunov exponent calculations indicate that P and D bifurcations have no direct connection.