Global dynamics of the stochastic Rabinovich system
Global dynamics of the stochastic Rabinovich system
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随机拉宾诺维奇系统的全局动力学
DOI：
10.1007/s11071-015-2131-0
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发表时间：
2015-05
影响因子：
5.6
通讯作者：
李丽洁
中科院分区：
文献类型：
--
作者：
刘爱民;李丽洁
本文分析比较了确定性Rabinovich系统的全局动力学和随机Rabinovich系统的全局动力学。首先简要回顾并分析了确定性Rabinovich系统的重要特征，然后给出了该系统的全局指数吸引集和正不变集.其次，利用随机微分方程理论和李雅普诺夫函数，讨论了Itô型随机Rabinovich系统和Stratonovich型随机Rabinovich系统的渐近性态和全局指数吸引集.第三，为了清楚地说明随机效应，分别对确定性情况和相应的随机情况进行了模拟。并通过R项目的Heidelberg和Welch试验对不稳定结果进行了数值验证。研究结果表明，在随机扰动下，Rabinovich系统的稳定性和全局指数吸引集发生了显著的变化。即使在相同的参数条件下，不同类型的随机微分方程的动力学性质也有明显的差异。进一步，从动力学和唯象的角度分析了Stratonovich型系统的随机音叉分岔。结果表明，平衡点随机分岔发生的位置会随着白色噪声强度的变化而变化。
In this paper, the global dynamics of the deterministic Rabinovich system and the dynamics of the stochastic Rabinovich are analyzed and compared. First, the important feature of the deterministic Rabinovich system is briefly recalled and analyzed; then the globally exponentially attractive set and positive invariant set of the system are given. Second, by using the theory of stochastic differential equation and the Lyapunov function, the asymptotic behavior and the globally exponentially attractive set of the Itô-type stochastic Rabinovich system and the Stratonovich-type stochastic Rabinovich system are discussed. Third, to illustrate the stochastic effects clearly, simulations for the deterministic case and corresponding stochastic case are performed, respectively. And the unstable results are numerically verified through the Heidelberg and Welch test by R project. The obtaining results show that the stability and the globally exponentially attractive set of the Rabinovich system occur change significantly under stochastic disturbance. Even under the same parameter conditions, the dynamics of the different-type stochastic differential equation has marked differences. Further, from the dynamical and phenomenological point, the stochastic pitchfork bifurcation of the Stratonovich-type system is analyzed. Results show the position where the stochastic bifurcation at the equilibrium point occurs will change as the intensity of the white noise change.
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