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基于线性随机系统Khasminskii球面坐标变换, 计算了谐和激励中含有随机相位的Duffing 方程的最大Lyapunov指数. 依据平均最大Lyapunov指数符号的变化, 分析随机相位对非线性系统动力学行为的影响.说明随机相位可以产生混沌亦可抑制混沌, 从而可以作为混沌控制的一种方法. 结合对相图、Poincaré截面、时间历程图的分析, 说明上述方法是有效的.
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关键词:
- 随机相位 /
- 混沌控制 /
- 最大Lyapunov指数 /
- Poincaré截面
In this paper, the effect of random phase for Duffing systems is investigated. We show that random phase can generate chaos or suppress chaos by the average of top Lyapunov exponent, which is computed based on Khasminskii's spherical coordinate formulation for linear stochastic systems. In addition, phase portraits, Poincaré surface of section and time evolution are studied to confirm the obtained results. Both methods lead to fully consistent results.
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