摘要
本文研究了具有同宿轨道、异宿轨道φ6势的Duffing振子在谐和激励与高斯白噪声激励联合作用下的混沌运动.基于同宿分叉和异宿分叉,由Melnikov理论推导了系统存在混沌的必要条件以及出现分形域边界的充分条件.结果表明:噪声的存在,降低了混沌运动的阈值,增大了参数空间的混沌域.进一步的研究发现,随着噪声幅值的增大,导致混沌运动的谐和激励的临界幅值单调减小.最后,数值模拟了系统的Lyapunov指数,由最大Lyapunov指数为零得到了系统产生混沌运动的另一个阈值,并且发现此阈值也随着噪声幅值单调减小.最后进一步用Poincare截面研究了噪声对系统运动的影响.
The chaotic behaviors of a particle in a triple potential well possessing both homoclinic and heteroclinic orbits under harmonic and Gaussian white noise excitations were studied. Following the Melnikov theory, the conditions for the existence of transverse intersection on the surface of homoclinic or heteroclinic orbits for the triple potential well case were derived, and were complemented by the numerical simulations, from which we showed the bifurcation surfaces and the fractaiity of the basins of attraction. The results revealed that the threshold amplitude of harmonic excitation for onset of chaos moved downwards as the noise intensity increasesd, which was further verified by the top Lyapunov exponents of the original system. Thus the larger the noise intensity, the more possible chaotic domain in the parameter space. Moreover,the effect of noise on Poincare maps was also investigated.
出处
《动力学与控制学报》
2005年第3期13-22,共10页
Journal of Dynamics and Control
基金
国家自然科学基金项目(10472091)
国家重点自然科学基金项目(10332030)
陕西省自然科学基金资助
