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Advances and Applications in Chaotic Systems pp 137–161Cite as

A Seven-Term Novel Jerk Chaotic System and Its Adaptive Control

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 636))

Abstract

In this work, we describe a seven-term novel 3-D jerk chaotic system with two nonlinearities (quadratic and cubic). The phase portraits of the novel jerk chaotic system are displayed and the dynamic properties of the novel jerk chaotic system are discussed. The novel jerk chaotic system has three saddle-foci equilibrium points, which are unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as \(L_1 = 0.5565, L_2 = 0\) and \(L_3 = -1.5566\). The Kaplan–Yorke dimension of the novel jerk chaotic system is obtained as \(D_{KY} = 2.3575\). Next, an adaptive backstepping controller is designed to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown 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 systems. MATLAB simulations have been shown to illustrate all the main results derived in this work.

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

    Sundarapandian Vaidyanathan

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

    Sundarapandian Vaidyanathan

  2. Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Christos Volos

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Vaidyanathan, S. (2016). A Seven-Term Novel Jerk Chaotic System and Its Adaptive Control. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_6

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