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Advances in Chaos Theory and Intelligent Control pp 155–178Cite as

Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities

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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 an eight-term 3-D novel chaotic system with three quadratic nonlinearities. First, this work describes the dynamic analysis of the novel chaotic system. The Lyapunov exponents of the eight-term novel chaotic system are obtained as \(L_1 = 4.0359, L_2 = 0\) and \(L_3 = -29.1071\). The Kaplan-Yorke dimension of the novel chaotic system is obtained as \(D_{KY} = 2.1384\). Next, this work describes the adaptive feedback control of the novel chaotic system with unknown parameters. Also, this work describes the adaptive feedback synchronization of the identical novel 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 eight-term 3-D novel 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, Banha, 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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  1. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S., Azar, A.T. (2016). Dynamic Analysis, Adaptive Feedback Control and Synchronization of An Eight-Term 3-D Novel Chaotic System with Three Quadratic Nonlinearities. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-30340-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30338-3

  • Online ISBN: 978-3-319-30340-6

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