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Adaptive Control and Circuit Simulation of a Novel 4-D Hyperchaotic System with Two Quadratic Nonlinearities

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Advances and Applications in Chaotic Systems

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

Abstract

This work describes a ten-term novel 4-D hyperchaotic system with two quadratic nonlinearities. The phase portraits of the 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 \(L_1 = 1.0784, L_2 = 0.1114, L_3 = 0\) and \(L_4 = -18.1714\), while the Kaplan–Yorke dimension of the novel hyperchaotic system is obtained as \(D_{KY} = 3.0655\). 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. Moreover, 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. Finally, an electronic circuit realization of the novel hyperchaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.

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Authors and Affiliations

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

    Sundarapandian Vaidyanathan

  2. Physics Department, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Christos K. Volos

  3. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

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  1. Sundarapandian Vaidyanathan
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  2. Christos K. Volos
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  3. Viet-Thanh Pham
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Correspondence to Sundarapandian Vaidyanathan .

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Editors and Affiliations

  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., Volos, C.K., Pham, VT. (2016). Adaptive Control and Circuit Simulation of a Novel 4-D Hyperchaotic System with Two Quadratic Nonlinearities. 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_7

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  • DOI: https://doi.org/10.1007/978-3-319-30279-9_7

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