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2016 | OriginalPaper | Buchkapitel

Adaptive Control and Synchronization of Halvorsen Circulant Chaotic Systems

verfasst von : Sundarapandian Vaidyanathan, Ahmad Taher Azar

Erschienen in: Advances in Chaos Theory and Intelligent Control

Verlag: Springer International Publishing

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Abstract

In this research work, we describe Halvorsen circulant chaotic systems and its qualitative properties. We show that Halvorsen circulant chaotic system is dissipative and that it has an unstable equilibrium at the origin. The Lyapunov exponents of Halvorsen circulant chaotic system are obtained as \(L_1 =0.8109\), \(L_2 = 0\) and \(L_3 = -4.6255\). The Kaplan-Yorke dimension of the Halvorsen circulant chaotic system is obtained as \(D_{KY} = 2.1753\). Next, this work describes the adaptive control of the Halvorsen circulant chaotic system with unknown parameters. Also, this work describes the adaptive synchronization of the identical Halvorsen circulant chaotic systems with unknown parameters. The adaptive feedback control and synchronization results are proved using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results for the Halvorsen circulant chaotic system.

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Metadaten
Titel
Adaptive Control and Synchronization of Halvorsen Circulant Chaotic Systems
verfasst von
Sundarapandian Vaidyanathan
Ahmad Taher Azar
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-30340-6_10