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Fractional-order two-component oscillator: stability and network synchronization using a reduced number of control signals

Author

Listed:
  • Romanic Kengne

    (Research Group on Experimental and Applied Physics for Sustainable Development, Faculty of Science, Department of Physics, University of Dschang
    Laboratory of Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang)

  • Robert Tchitnga

    (Research Group on Experimental and Applied Physics for Sustainable Development, Faculty of Science, Department of Physics, University of Dschang
    Laboratory of Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang
    Institute of Surface Chemistry and Catalysis, University of Ulm)

  • Alain Kammogne Soup Tewa

    (Laboratory of Electronics and Signal Processing Faculty of Science, Department of Physics, University of Dschang)

  • Grzegorz Litak

    (Lublin University of Technology, Faculty of Mechanical Engineering
    AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Department of Process Control)

  • Anaclet Fomethe

    (Laboratoire de Mécanique et de Modélisation des Systèmes, L2MS, Department of Mathematics and Computer Science, Faculty of Science, University of Dschang)

  • Chunlai Li

    (College of Physics and Electronics, Hunan Institute of Science and Technology Yueyang)

Abstract

In this paper, a fractional-order version of a chaotic circuit made simply of two non-idealized components operating at high frequency is presented. The fractional-order version of the Hopf bifurcation is found when the bias voltage source and the fractional-order of the system increase. Using Adams–Bashforth–Moulton predictor–corrector scheme, dynamic behaviors are displayed in two complementary types of stability diagrams, namely the two-parameter Lyapunov exponents and the isospike diagrams. The latest being a more fruitful type of stability diagrams based on counting the number of spikes contained in one period of the periodic oscillations. These two complementary types of stability diagrams are reported for the first time in the fractional-order dynamical systems. Furthermore, a new fractional-order adaptive sliding mode controller using a reduced number of control signals was built for the stabilization of a fractional-order complex dynamical network. Two examples are shown on a fractional-order complex dynamical network where the nodes are made of fractional-order two-component circuits. Firstly, we consider an ideal channel, and secondly, a non ideal one. In each case, increasing of the coupling strength leads to the phase transition in the fractional-order complex network. Graphical abstract

Suggested Citation

  • Romanic Kengne & Robert Tchitnga & Alain Kammogne Soup Tewa & Grzegorz Litak & Anaclet Fomethe & Chunlai Li, 2018. "Fractional-order two-component oscillator: stability and network synchronization using a reduced number of control signals," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 91(12), pages 1-19, December.
    • Handle: RePEc:spr:eurphb:v:91:y:2018:i:12:d:10.1140_epjb_e2018-90362-7
    DOI: 10.1140/epjb/e2018-90362-7
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    Cited by:

    1. Tene, Alain Giresse & Tchoffo, Martin & Tabi, Bertrand Conrad & Kofane, Timoleon Crepin, 2020. "Generalized synchronization of regulate seizures dynamics in partial epilepsy with fractional-order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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    Keywords

    Statistical and Nonlinear Physics;

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