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Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems

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Chaos Modeling and Control Systems Design

Part of the book series: Studies in Computational Intelligence ((SCI,volume 581))

Abstract

This research work investigates the global chaos synchronization of Sprott’s jerk chaotic system using backstepping control method. Sprott’s jerk system (1997) is algebraically the simplest dissipative chaotic system consisting of five terms and a quadratic nonlinearity. Sprott’s chaotic system involves only five terms and one quadratic nonlinearity, while Rössler’s chaotic system (1976) involves seven terms and one quadratic nonlinearity. This work first details the properties of the Sprott’s jerk chaotic system. The phase portraits of the Sprott’s jerk system are described. The Lyapunov exponents of the Sprott’s jerk system are obtained as L 1 = 0.0525, L 2 = 0 and L 3 = −2.0727. The Lyapunov dimension of the Sprott’s jerk system is obtained as D L  = 2.0253. Next, an active backstepping controller is designed for the global chaos synchronization of identical Sprott’s jerk systems with known parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict-feedback chaotic systems. Finally, an adaptive backstepping controller is designed for the global chaos synchronization of identical Sprott’s jerk systems with unknown parameters. MATLAB simulations are provided to validate and demonstrate the effectiveness of the proposed active and adaptive chaos synchronization schemes for the Sprott’s jerk systems.

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Authors and Affiliations

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

    Sundarapandian Vaidyanathan

  2. Department of Physics, Lagos State University, Lagos, Nigeria

    Babatunde A. Idowu

  3. Faculty of Computers and Information, Benha University, Banha, Egypt

    Ahmad Taher Azar

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  1. Sundarapandian Vaidyanathan
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  2. Babatunde A. Idowu
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  3. Ahmad Taher Azar
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Correspondence to Sundarapandian Vaidyanathan .

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

    Ahmad Taher Azar

  2. Research and Development Centre, Vel Tech University, Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S., Idowu, B.A., Azar, A.T. (2015). Backstepping Controller Design for the Global Chaos Synchronization of Sprott’s Jerk Systems. In: Azar, A., Vaidyanathan, S. (eds) Chaos Modeling and Control Systems Design. Studies in Computational Intelligence, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-13132-0_3

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  • DOI: https://doi.org/10.1007/978-3-319-13132-0_3

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