基于Laguerre多项式逼近法的随机双势阱Duffing系统的分岔和混沌研究

Analysis of bifurcation and chaos in double-well Duffing system via Laguerre polynomial approximation

应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统,然后通过数值方法求得其响应.数值模拟结果的比较表明,含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为,但是由于随机因素的影响,在局部小区域内随机参数系统的动力学行为会发生突变.

Laguerre polynomial approximation method is applied to study the period-doubling bifurcation and chaos behavior in doublewell Duffing system with a random parameter subjected to harmonic excitation. Firstly the stochastic system is reduced to its equivalent deterministic counterpart, through which the response of the stochastic system can be obtained by numerical methods. Then bifurcation and chaos in the stochastic double-well Duffing system is explored. Numerical simulations show that the nonlinear dynamical behavior is similar to their counterpart in deterministic nonlinear system such as period-doubling bifurcation, but in some local areas they are shown to have their specific features.