Noise-induced chaos in the elastic forced oscillators with real-power damping force
Noise-induced chaos in the elastic forced oscillators with real-power damping force
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DOI：
10.1007/s11071-012-0672-z
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发表时间：
2013-02
影响因子：
5.6
通讯作者：
Di Liu;Wei Xu;Yong Xu
中科院分区：
文献类型：
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作者：
Di Liu;Wei Xu;Yong Xu
研究了有界噪声作用下阻尼项和恢复力项均为实幂指数的弹性受迫振子的混沌行为。利用随机Melnikov方法，利用均方判据确定了该随机系统混沌运动的必要条件。结果表明，系统进入混沌的有界噪声幅值阈值随随机频率强度的增大而增大，随阻尼项实幂指数的增大而减小。通过最大李雅普诺夫指数的数值计算，确定了混沌发生的有界噪声幅值阈值。研究了有界噪声和阻尼项的实幂指数对分岔和Poincaré映射的影响。我们的结果对于理解有界噪声对一类广义双势阱系统的影响具有重要的指导意义。
The chaotic behavior of the elastic forced oscillators with real-power exponents of damping and restoring force terms under bounded noise is investigated. By using random Melnikov method, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the random frequency increases, and decrease as the real-power exponent of damping term increase. The threshold of bounded noise amplitude for the onset of chaos is determined by the numerical calculation via the largest Lyapunov exponents. The effects of bounded noise and real-power exponent of damping term on bifurcation and Poincaré map are also investigated. Our results may provide a valuable guidance for understanding the effect of bounded noise on a class of generalized double well system.