一类非线性振子中有界噪声诱发的混沌运动

Chaotic Motions Induced by Bounded Noise in a Nonlinear Oscillator

研究谐和外力与有界噪声激励联合作用下的一类非线性振子的混沌运动。利用 Melnikov方法 ,通过计算扰动系统的 Melnikov积分 ,分析了系统在参数发生变化时的同宿分岔 ,得出系统产生混沌运动的参数阈值 ,并讨论了有界噪声激励对系统的混沌运动的影响。最后利用数值方法模拟了系统的安全盆的侵蚀状况 ,并进一步通过计算系统运动的 L yapunov指数 ,给出了由噪声诱发的混沌运动与噪声激励下非混沌运动之间的差别。

This paper studies chaotic motions in a nonlinear oscillatory system perturbed by external harmonic force and bounded noise excitation. By using the Melnikov method, the system's Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Then the system's homoclinic bifurcation is analyzed and the effects of bounded noise on chaotic motions are also discussed. Safe basins and motions of the system are simulated by Monte-Carlo and Runge-Kutta methods. Moreover, the Lyapunov exponents of the system's motions are computed, by which the differences between noise-induced chaotic motion and non-chaotic motions under the excitation of bounded noise are given.