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Analysis of a 4-D Hyperchaotic Fractional-Order Memristive System with Hidden Attractors

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Advances in Memristors, Memristive Devices and Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 701))

Abstract

In 1695, G. Leibniz laid the foundations of fractional calculus, but mathematicians revived it only 300 years later. In 1971, L.O. Chua postulated the existence of a fourth circuit element, called memristor, but Williams’s group of HP Labs realized it only 37 years later. In recent years, few unusual dynamical systems, such as those with a line of equilibriums, with stable equilibria or without equilibrium, which belong to chaotic systems with hidden attractors, have been reported. By looking at these interdisciplinary and promising research areas, in this chapter, a fractional-order 4-D memristive system with a line of equilibria is introduced. In particular, a hyperchaotic behavior in a simple fractional-order memristor-based system is presented. Systematic studies of the hyperchaotic behavior in the integer and fractional-order form of the system are performed using phase portraits, Poincaré maps, bifurcation diagrams and Lyapunov exponents. Simulation results show that both integer-order and fractional-order system exhibit hyperchaotic behavior over a wide range of control parameter. Finally, the electronic circuits for the evaluation of the theoretical model of the proposed integer and fractional-order systems are presented.

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Authors and Affiliations

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

    Christos Volos

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

    V.-T. Pham

  3. Department of Applied Mathematics, IPICYT, San Luis Potosi, SLP, 78216, San Luis Potosí, Mexico

    E. Zambrano-Serrano

  4. Electronics Department, Autonomous University of Puebla (BUAP), 72570, Puebla, Mexico

    J. M. Munoz-Pacheco

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

    Sundarapandian Vaidyanathan

  6. Department of Electronics, INAOE, Tonantzintla Puebla, 72840, Cholula, Mexico

    E. Tlelo-Cuautle

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  1. Christos Volos
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  2. V.-T. Pham
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  3. E. Zambrano-Serrano
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  1. Research and Development Centre, Vel Tech University Research and Development Centre, Chennai, India

    Sundarapandian Vaidyanathan

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

    Christos Volos

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Volos, C., Pham, VT., Zambrano-Serrano, E., Munoz-Pacheco, J.M., Vaidyanathan, S., Tlelo-Cuautle, E. (2017). Analysis of a 4-D Hyperchaotic Fractional-Order Memristive System with Hidden Attractors. In: Vaidyanathan, S., Volos, C. (eds) Advances in Memristors, Memristive Devices and Systems. Studies in Computational Intelligence, vol 701. Springer, Cham. https://doi.org/10.1007/978-3-319-51724-7_9

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