Hyperchaos synchronization using univariate impulse control

Kun Tian, Chao Bai, Hai-Peng Ren* (Corresponding Author), Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticle

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Abstract

Rössler and Chen systems with time delay are shown to be hyperchaotic, which exhibits a more complex dynamics, including multiple positive Lyapunov exponents and infinite dimension. The hyperchaos has better application potential where hyperchaos synchronization is concerned. Univariate impulse control requires smaller perturbation to the response system, thus promising better performance. However, synchronization of two hyperchaotic systems using this control method is a challenging task due to the difficulty to guarantee synchronization stability using a minimum number of manipulated variables. In this paper, a univariate impulse control method is proposed for the synchronization of two hyperchaotic dynamics generated by time delay. A theorem is developed and proved to provide the sufficient conditions for the synchronization of time delay systems using the univariate impulse control. The upper bound of the impulse interval is proved to guarantee the asymptotic synchronization. Simulation and circuit experiment show the correctness of the analysis and the feasibility of the proposed method.
Original languageEnglish
Article number052215
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume100
Issue number5
Early online date25 Nov 2019
DOIs
Publication statusPublished - Nov 2019

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Hyperchaos
Impulse Control
Univariate
impulses
synchronism
Synchronization
time lag
Time Delay
Chen System
Hyperchaotic System
Infinite Dimensions
Time-delay Systems
Complex Dynamics
Small Perturbations
Impulse
Lyapunov Exponent
Correctness
theorems
exponents
Upper bound

Keywords

  • DYNAMICS
  • CHAOS
  • STABILIZATION
  • CIRCUIT

Cite this

Hyperchaos synchronization using univariate impulse control. / Tian, Kun ; Bai, Chao ; Ren, Hai-Peng (Corresponding Author); Grebogi, Celso.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 100, No. 5, 052215, 11.2019.

Research output: Contribution to journalArticle

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AB - Rössler and Chen systems with time delay are shown to be hyperchaotic, which exhibits a more complex dynamics, including multiple positive Lyapunov exponents and infinite dimension. The hyperchaos has better application potential where hyperchaos synchronization is concerned. Univariate impulse control requires smaller perturbation to the response system, thus promising better performance. However, synchronization of two hyperchaotic systems using this control method is a challenging task due to the difficulty to guarantee synchronization stability using a minimum number of manipulated variables. In this paper, a univariate impulse control method is proposed for the synchronization of two hyperchaotic dynamics generated by time delay. A theorem is developed and proved to provide the sufficient conditions for the synchronization of time delay systems using the univariate impulse control. The upper bound of the impulse interval is proved to guarantee the asymptotic synchronization. Simulation and circuit experiment show the correctness of the analysis and the feasibility of the proposed method.

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