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Synchronization Phenomena in Coupled Hyperchaotic Oscillators with Hidden Attractors Using a Nonlinear Open Loop Controller

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Advances and Applications in Chaotic Systems

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

Abstract

In recent years the study of dynamical systems with hidden attractors, namely systems in which their basins of attraction do not intersect with small neighborhoods of equilibria, is a great challenge due to their application in many research fields such as in mechanics, secure communication and electronics. Especially, the investigation of hyperchaotic systems with hidden attractors plays a crucial role in this research approach. Motivated by the very complex dynamical behavior of hyperchaotic systems and the unusual features of hidden attractors, a bidirectionally and unidirectionally coupling scheme of systems of this family, by using a nonlinear open loop controller, is studied in this chapter. For this reason, a recently new proposed hyperchaotic system with hidden attractors, the four-dimensional modified Lorenz system, which is structurally the simplest hyperchaotic system with hidden attractors, is used. The simulation results show that the proposed scheme drives the coupled system either to complete synchronization or anti-synchronization depending on the choice of the signs of the error function’s parameters. In addition, an electronic circuit emulating the control scheme of the coupled hyperchaotic systems with hidden attractors is also presented to verify the feasibility of the proposed model.

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Authors and Affiliations

  1. Physics Department, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece

    Ch.K. Volos, I. M. Kyprianidis & I. N. Stouboulos

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

    V.-T. Pham

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

    S. Vaidyanathan

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  1. Ch.K. Volos
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  2. V.-T. Pham
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  3. S. Vaidyanathan
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  4. I. M. Kyprianidis
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  5. I. N. Stouboulos
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Correspondence to Ch.K. Volos .

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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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Volos, C., Pham, VT., Vaidyanathan, S., Kyprianidis, I.M., Stouboulos, I.N. (2016). Synchronization Phenomena in Coupled Hyperchaotic Oscillators with Hidden Attractors Using a Nonlinear Open Loop Controller. 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_1

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  • DOI: https://doi.org/10.1007/978-3-319-30279-9_1

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