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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.
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关键词:
- 非光滑系统 /
- 有界噪声 /
- 随机Melnokov函数 /
- 最大Lyapunov指数
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.-
Keywords:
- non-smooth dynamics /
- bounded noise /
- stochastic Melnikov function /
- maximal Lyapunov exponents
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中国物理学会期刊
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