非光滑周期扰动与有界噪声联合作用下受迫Duffing系统的混沌预测

考察了一类非光滑周期扰动和有界噪声联合作用下受迫Duffing系统的动力学行为. 对于非光滑扰动项，尝试采用Fourier级数展开的方法，得到与原系统等价的光滑系统. 在此基础上给出该系统的随机Melnikov函数，由Smale马蹄理论得到系统出现混沌的解析条件，并利用Poincaré截面、相图以及最大Lyapunov指数验证了理论结果. 关键词： 非光滑系统 有界噪声 随机Melnokov函数 最大Lyapunov指数

Chaos prediction in the Duffing-type system with non-smooth periodic perturbation and bounded parametric excitation

In this paper, the dynamics of Duffing-type system with non-smooth periodic perturbation and bounded noise was studied. The theory of Fourier series was used in this system to deal with the non-smooth character for the first time. The analytical condition for the appearance of chaos was given using stochastic Melnikov method. The numerical simulations confirm the validity of this method.