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Journal of Dynamical Systems and Geometric Theories

(Since 2002)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0057·ISSN (Print): 1726-037X

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Half-Yearly Journal: Publishes research on dynamical systems and geometry, including Random Dynamical Systems, hyperbolic behaviour, complex geometry and Ergodic theory.

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Journal of Dynamical Systems and Geometric Theories
Open Access Original Articles

Anti-Synchronization of the Four-Dimensional Hyperchaotic System with Uncertain Parameters Via Adaptive Control

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pp. 1–12Vol. 10Issue 1May 2012DOI: 10.1080/1726037X.2012.10698603XML
Received:
10 Jun 2011
Accepted:
12 Dec 2011
Published Online:
03 Jun 2013
Article type:
Original Articles
Language:
EN
Article no.:
1726037X.2012.10698603
Pages:
1–12

Abstract

In this paper, an adaptive control scheme is presented to study the anti-synchronization behavior between two identical four-dimensional hyperchaotic systems with unknown parameters. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Based on Lyapunov stability theory, an adaptive anti-synchronization controller is designed, and the analytic expression of the controller and the adaptive laws of parameters are developed. Numerical simulations are performed for four-dimensional hyperchaotic systems to demonstrate the effectiveness of the proposed control strategy.

Keywords

Four-dimensional hyperchaotic systemsAnti-synchronizationAdaptive controlLyapunov stability theory

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