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- Title
Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique.
- Authors
Munoz-Pacheco, Jesus M.; Volos, Christos; Serrano, Fernando E.; Jafari, Sajad; Kengne, Jacques; Rajagopal, Karthikeyan
- Abstract
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 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.
- Subjects
LORENZ equations; RHYTHM &; blues music; SYNCHRONIZATION; VECTOR fields; ATTRACTORS (Mathematics); FUNCTIONALS
- Publication
Entropy, 2021, Vol 23, Issue 7, p921
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e23070921