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Advances in Chaos Theory and Intelligent Control pp 225–247Cite as

Adaptive Control and Synchronization of Halvorsen Circulant Chaotic Systems

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 337))

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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Authors and Affiliations

  1. Research and Development Centre, Vel Tech University, Avadi, Chennai, 600062, Tamil Nadu, India

    Sundarapandian Vaidyanathan

  2. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

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  1. Sundarapandian Vaidyanathan
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  2. Ahmad Taher Azar
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Correspondence to Sundarapandian Vaidyanathan .

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Editors and Affiliations

  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S., Azar, A.T. (2016). Adaptive Control and Synchronization of Halvorsen Circulant Chaotic Systems. In: Azar, A., Vaidyanathan, S. (eds) Advances in Chaos Theory and Intelligent Control. Studies in Fuzziness and Soft Computing, vol 337. Springer, Cham. https://doi.org/10.1007/978-3-319-30340-6_10

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  • DOI: https://doi.org/10.1007/978-3-319-30340-6_10

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