北京理工大学 宇航学院力学系, 北京 100081
Department of Mechanics,Beijing Institute of Technology, Beijing 100081 , China
The project supported by the National Natural Science Foundation of China (11772048)
研究了相关乘性和加性高斯白噪声激励下，双稳态Duffing-Van der Pol系统的随机P-分岔和D-分岔；利用随机平均法，得出系统幅值稳态概率密度的理论表达式，以及随机P-分岔发生的临界参数条件；通过分析概率密度曲线形状的变化，发现阻尼系数、加性和乘性噪声强度均可诱导系统出现随机P-分岔，但对系统分岔区域的影响有着明显的不同，同时Monte-Carlo数值模拟验证了理论分析的有效性.此外，利用Wolf算法得到系统的最大Lyapunov指数，并分析了系统的稳定性和随机D-分岔，发现加性和乘性噪声强度以及阻尼系数
In this paper, the stochastic bifurcation in a bistable Duffing-Van der Pol oscillator driven by correlated multiplicative and additive Gaussian white noises was studied. By using the stochastic averaging method, the stationary probability density function of amplitude for the Duffing-Van der Pol oscillator and the critical parameter condition for stochastic P-bifurcation were obtained. Through the changes in the shape of stationary probability density function, it was found that both the damping coefficients and intensity of the multiplicative and additive noise may induce the stochastic P-bifurcation, but they have significantly different effects on the bifurcation regions. Meanwhile, the theoretical results were verified by Monte-Carlo simulations. Moreover, the largest Lyapunov exponent was calculated by the Wolf’s algorithm to evaluate the system stability. The results showed that both the increases of the coefficient of negative damping and the noise intensity can drive the system into an unstable state and induce D-bifurcation, and the system stability can be enhanced with increasing the coefficients of positive damping.
刘坤峰,靳艳飞.相关白噪声激励下双稳态Duffing-Van der Pol系统的随机分岔[J].动力学与控制学报,2020,18(4):12~18; Liu Kunfeng, JinYanfei. STOCHASTIC BIFURCATION IN BISTABLE DUFFING-VAN DER POL SYSTEM DRIVEN BY CORRELATED WHITE NOISES[J]. Journal of Dynamics and Control,2020,18(4):12-18.复制