Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique

Entropy

卷:23

Karthikeyan Rajagopal¹  Jacques Kengne²  Jesus M. Munoz-Pacheco³  Fernando E. Serrano⁴  Christos Volos⁵  Sajad Jafari⁶ 

[1] Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India;

[2] Department of Electrical Engineering, University of Dschang, Dschang P.O. Box 134, Cameroon;

[3] Faculty of Electronics Sciences, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Mexico;

[4] Instituto de Investigacion en Energia IIE, Universidad Nacional Autonoma de Honduras (UNAH), Tegucigalpa 11101, Honduras;

[5] Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;

[6] Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam;

关键词: chaotic systems;    hidden attractors;    backstepping controller;    synchronization;    stabilization;   

DOI  :  10.3390/e23070921

来源: DOAJ

【 摘 要 】

In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the ${\mathbb{C}}^n$ domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.

【 授权许可】

Unknown