Stabilizing near-nonhyperbolic chaotic systems with applications
Stabilizing near-nonhyperbolic chaotic systems with applications
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DOI：
10.1103/physrevlett.93.214101
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发表时间：
2004-11-19
影响因子：
8.6
通讯作者：
Huang, DB
中科院分区：
文献类型：
--
作者：
Huang, DB
基于微分方程组的不变性原理，提出了一种简单、系统、反馈强度可变的严格反馈方案，使非线性有限维混沌系统镇定，且不需要任何系统的先验分析知识。特别是，这种方法可以用于控制接近非双曲的混沌系统，尽管这种系统自然地产生于天体物理学的模型和神经生物学的模型，但所有的Ott-Grebogi-York类型的方法都将无法稳定。该方法分别成功地应用于著名的Hindmarsh-Rose神经元模型、Fitzhugh-Rinzel神经元模型和Rossler超混沌系统。
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly finite-dimensional chaotic systems without any prior analytical knowledge of the systems. Especially the method may be used to control near-nonhyperbolic chaotic systems, which, although arising naturally from models in astrophysics to those for neurobiology, all Ott-Grebogi-York type methods will fail to stabilize. The technique is successfully used for the famous Hindmarsh-Rose neuron model, the FitzHugh-Rinzel neuron model, and the Rossler hyperchaos system, respectively.