含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔

讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统，然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为，同时指出，随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法. 关键词： Chebyshev多项式 随机Duffing-van der Pol系统 倍周期分岔

Period-doubling bifurcation of a double-well Duffing-van der Pol system with bounded random parameters

Period-doubling bifurcation in a double-well Duffing-van der Pol system with bounded random parameters and subject to harmonic excitations is studied. The random system is reduced to its equivalent deterministic one by the Chebyshev polynomial approximation, through which the response of the random system can be obtained by deterministic numerical methods. Numerical simulations show that similar to their counterparts in deterministic nonlinear systems, period-doubling bifurcation may occur in the random Duffing-van der Pol system, and that the period-doubling bifurcation of the random_parameter system has its own characteristics. Numerical results also show that the Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear systems with random parameters.