Department of Mathematics, Ural State University, Lenina, 51, Ekaterinburg, Russia.
Chaos. 2012 Sep;22(3):033104. doi: 10.1063/1.4732543.
The stochastically perturbed Chen system is studied within the parameter region which permits both regular and chaotic oscillations. As noise intensity increases and passes some threshold value, noise-induced hopping between close portions of the stochastic cycle can be observed. Through these transitions, the stochastic cycle is deformed to be a stochastic attractor that looks like chaotic. In this paper for investigation of these transitions, a constructive method based on the stochastic sensitivity function technique with confidence ellipses is suggested and discussed in detail. Analyzing a mutual arrangement of these ellipses, we estimate the threshold noise intensity corresponding to chaotization of the stochastic attractor. Capabilities of this geometric method for detailed analysis of the noise-induced hopping which generates chaos are demonstrated on the stochastic Chen system.
本文研究了在允许正则和混沌振荡的参数区域内的随机摄动 Chen 系统。随着噪声强度的增加并超过某个阈值，可以观察到随机周期的接近部分之间的噪声诱导的跳跃。通过这些转变，随机周期变形为看起来像混沌的随机吸引子。在本文中，为了研究这些转变，提出并详细讨论了一种基于具有置信椭圆的随机灵敏度函数技术的构造方法。通过分析这些椭圆的相互排列，我们估计了对应于随机吸引子混沌化的阈值噪声强度。该几何方法用于详细分析产生混沌的噪声诱导跳跃的能力在随机 Chen 系统上得到了验证。
