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Generalized chaos control and synchronization by nonlinear high-order approach

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  • Boukabou, Abdelkrim
  • Mekircha, Naim

Abstract

This paper investigates the generalized control and synchronization of chaotic dynamical systems. First, we show that it is possible to stabilize the unstable periodic orbits (UPOs) when we use a high-order derivation of the OGY control that is known as one of useful methods for controlling chaotic systems. Then we examine synchronization of identical chaotic systems coupled in a master/slave manner. A rigorous criterion based on the transverse stability is presented which, if satisfied, guarantees that synchronization is asymptotically stable. The Rössler attractor and Chen system are used as examples to demonstrate the effectiveness of the developed approach and the improvement over some existing results.

Suggested Citation

  • Boukabou, Abdelkrim & Mekircha, Naim, 2012. "Generalized chaos control and synchronization by nonlinear high-order approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2268-2281.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:11:p:2268-2281
    DOI: 10.1016/j.matcom.2012.07.005
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    References listed on IDEAS

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    1. Wan, Xiaojun & Sun, Jitao, 2011. "Adaptive–impulsive synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1609-1617.
    2. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "A multiparameter chaos control method based on OGY approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1376-1390.
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    Cited by:

    1. Garza-González, E. & Posadas-Castillo, C. & López-Mancilla, D. & Soriano-Sánchez, A.G., 2020. "Increasing synchronizability in a scale-free network via edge elimination," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 233-243.
    2. Arbid, Mahmoud & Teffahi, Abdelkader & Boukabou, Abdelkrim & Bounar, Amel, 2023. "Predictive-based control of complex dynamic networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Soriano-Sánchez, A.G. & Posadas-Castillo, C. & Platas-Garza, M.A. & Diaz-Romero, D.A., 2015. "Performance improvement of chaotic encryption via energy and frequency location criteria," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 112(C), pages 14-27.
    4. Senouci, Abdelkader & Boukabou, Abdelkrim, 2014. "Predictive control and synchronization of chaotic and hyperchaotic systems based on a T–S fuzzy model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 62-78.

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