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

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 Cn domain. Then, considering first the original...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2021-07, Vol.23 (7), p.921
Main Authors: Munoz-Pacheco, Jesus M., Volos, Christos, Serrano, Fernando E., Jafari, Sajad, Kengne, Jacques, Rajagopal, Karthikeyan
Format: Article
Language:English
Subjects:
Attraction
Attractors (mathematics)
backstepping controller
Chaos theory
chaotic systems
Domains
Electromagnetism
Equilibrium
Feedback
Fields (mathematics)
Fuzzy logic
hidden attractors
Lorenz system
Mathematical analysis
Recursive methods
Stabilization
Synchronism
synchronization
Topology
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Summary: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 Cn 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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e23070921