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Advances in Chaos Theory and Intelligent Control pp 179–202Cite as

Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic 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 work, we announce an eleven-term novel 4-D hyperchaotic system with three quadratic nonlinearities. The phase portraits of the eleven-term novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel hyperchaotic system has a unique equilibrium at the origin, which is a saddle point. The Lyapunov exponents of the novel hyperchaotic system are obtained as \(L_1 = 2.0836\), \(L_2 = 0.1707\), \(L_3 = 0\) and \(L_4 = -26.6499\). The maximal Lyapunov exponent of the novel hyperchaotic system is found as \(L_1 = 2.0836\). Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is derived as \(D_{KY} = 3.0846\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. Finally, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work.

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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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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). Qualitative Study and Adaptive Control of a Novel 4-D Hyperchaotic 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_8

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