Xu Yong, Gu Rencai, Zhang Huiqing, Xu Wei, Duan Jinqiao
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056215. doi: 10.1103/PhysRevE.83.056215. Epub 2011 May 26.
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.
本文旨在研究高斯色噪声诱导的双稳杜芬 - 范德波尔振子中的随机分岔以及相关时间和噪声强度的动力学影响。理论上，通过使用随机平均法，可以得到杜芬 - 范德波尔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。通过平稳概率分布的定性变化来讨论随机分岔，这表明系统参数、噪声强度和噪声相关时间分别可被视为分岔参数。它们还意味着乘性噪声的影响与加性噪声的影响有很大不同。直接数值模拟结果验证了理论分析的有效性。此外，最大李雅普诺夫指数计算表明P分岔和D分岔没有直接联系。
