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Hyperchaos, Control, Synchronization and Circuit Simulation of a Novel 4-D Hyperchaotic System with Three Quadratic Nonlinearities

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Advances in Chaos Theory and Intelligent Control

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 novel 4-D hyperchaotic system has been derived by adding a feedback control to the seven term 3-D Lu-Xiao chaotic system [1]. 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. Thus, the origin is an unstable equilibrium of the novel hyperchaotic system. The Lyapunov exponents of the novel hyperchaotic system are obtained as \(L_1 = 1.6023, L_2 = 0.1123, L_3 = 0\) and \(L_4 = -22.6467\). Also, the Kaplan-Yorke dimension of the novel hyperchaotic system is obtained as \(D_{KY} = 3.0757\). 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. Finally, an electronic circuit realization of the novel 4-D hyperchaotic system using SPICE is described 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, Thessaloniki, GR-54124, 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

Authors
  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. Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Chennai, India

    Sundarapandian Vaidyanathan

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Vaidyanathan, S., Volos, C.K., Pham, VT. (2016). Hyperchaos, Control, Synchronization and Circuit Simulation 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_13

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  • DOI: https://doi.org/10.1007/978-3-319-30340-6_13

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