A new thermally excited chaotic jerk system, its dynamical analysis, adaptive backstepping control, and circuit simulation

Vaidyanathan, Sundarapandian; Sambas, Aceng; Azar, Ahmad Taher; Serrano, Fernando E.; Fekik, Arezki

doi:10.1016/b978-0-12-817582-8.00015-5

Cited by 6 publications

(1 citation statement)

References 37 publications

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“…Then, in [ 19 ] the backstepping control circuit design of a plasma torch chaotic system is presented. In [ 20 ] a new thermally excited chaotic jerk system with its adaptive backstepping control and circuit simulation is shown. Another example can be found in papers like [ 21 ] in which nonlinear resonant velocity feedback controller is used to stabilize self-excited vibrations in a nonlinear beam.…”

Section: Introductionmentioning

confidence: 99%

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

Muñoz‐Pacheco

Volos

Serrano

et al. 2021

Entropy

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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.

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Section: Introductionmentioning

confidence: 99%