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On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations

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  • Kengne, Romanic
  • Tchitnga, Robert
  • Mabekou, Sandrine
  • Tekam, Blaise Raoul Wafo
  • Soh, Guy Blondeau
  • Fomethe, Anaclet

Abstract

The relay coupling of three fractional-order two-stage oscillators in the presence of time delay has been explored theoretically, numerically and analogically. The global stabilization of the system in a finite time is proven through Hölder and Gronwall inequalities, as well as through inequality scaling skills. The Synchronization of the system is characterized in terms of its parameters (coupling strength and time delay) by using time series, two parameters phase diagrams and two parameters transverse Lyapunov exponent diagrams. It is found that for smaller delay values, the network exhibits global phase synchronization whereas for higher delay values, phase synchronization just occurs between the two indirectly connected units (cluster phase synchronization). Striking phenomena such as amplitudes’ death and chaotic beats oscillations are also observed from this relay coupling of three fractional-order two-stage oscillators. Furthermore, PSpice simulation results of the analog electronic circuit are in perfect accordance with both theoretical and numerical results.

Suggested Citation

  • Kengne, Romanic & Tchitnga, Robert & Mabekou, Sandrine & Tekam, Blaise Raoul Wafo & Soh, Guy Blondeau & Fomethe, Anaclet, 2018. "On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 6-17.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:6-17
    DOI: 10.1016/j.chaos.2018.03.040
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    References listed on IDEAS

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    1. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    2. Seng-Kin Lao & Lap-Mou Tam & Hsien-Keng Chen & Long-Jye Sheu, 2014. "Hybrid Stability Checking Method for Synchronization of Chaotic Fractional-Order Systems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-11, April.
    3. Romanic Kengne & Robert Tchitnga & Anicet Mezatio & Anaclet Fomethe & Grzegorz Litak, 2017. "Finite-time synchronization of fractional-order simplest two-component chaotic oscillators," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(5), pages 1-10, May.
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    Cited by:

    1. Zhang, Zhe & Ai, Zhaoyang & Zhang, Jing & Cheng, Fanyong & Liu, Feng & Ding, Can, 2020. "A general stability criterion for multidimensional fractional-order network systems based on whole oscillation principle for small fractional-order operators," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Wafo Tekam, Raoul Blaise & Kengne, Jacques & Djuidje Kenmoe, Germaine, 2019. "High frequency Colpitts’ oscillator: A simple configuration for chaos generation," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 351-360.
    3. Mezatio, Brice Anicet & Motchongom, Marceline Tingue & Wafo Tekam, Blaise Raoul & Kengne, Romanic & Tchitnga, Robert & Fomethe, Anaclet, 2019. "A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 100-115.
    4. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.

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