Chaotic system with coexisting attractors and the stabilization of its fractional order system

被引：4
|
作者：
Xian Y.-J. [1 ]
Xia C. [1 ]
Zhong D. [1 ]
Xu C.-B. [2 ]
机构：
[1] School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing
[2] School of Optoelectronic Engineering, Chongqing University of Posts and Telecommunications, Chongqing
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2019年 / 36卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Chaos control; Chaotic system; Coexisting attractors; Fractional order system; Topological horseshoe;
D O I：
10.7641/CTA.2018.70943
中图分类号：
学科分类号：
摘要：
A chaotic system with coexisting attractors and the stabilization problem of the corresponding fractional order system are studied. A novel chaotic system with the existence of double-wing and four-wing chaotic attractors is proposed. Its math characteristics are investigated by Lyapunov exponents spectrum and bifurcation diagram. By means of topological horseshoe theory and numerical computation, the topological horseshoe and the topological entropy in the system are obtained. Based on the system, a new 3D fractional order chaotic system is constructed. The fractional order system also has two isolated double-wing attractors and four-wing attractors, and there are not overlaps between the coexisting double wing attractors. For the stabilization of the fractional order system, a linear feedback scalar controller is designed. The nonlinear terms in the system are not deleted by the controlling method. The theoretical analysis and numerical simulation show the effectiveness of the method. © 2019, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
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页码：262 / 270
页数：8
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