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Synchronization of Chaotic Systems with Huygens-like Coupling

Author

Listed:
  • Jonatan Pena Ramirez

    (Applied Physics Division, Department of Electronics and Telecommunications, CICESE, Carr. Ensenada-Tijuana 3918, Zona Playitas, Ensenada 22860, Mexico)

  • Adrian Arellano-Delgado

    (National Council of Humanities, Science and Technology (CONAHCYT), Ciudad de Mexico 03940, Mexico
    Engineering, Architecture and Design Faculty, Autonomous University of Baja California, Ensenada 22860, Mexico)

  • Rodrigo Méndez-Ramírez

    (Paradigm Advance Research Center (PARC), 5340 Canotek Rd., Unit #4, Ottawa, ON K1J9C6, Canada)

  • Hector Javier Estrada-Garcia

    (Engineering Division Campus Irapuato-Salamanca, University of Guanajuato, Carr. Salamanca-Valle de Santiago km 3.5 + 1.8, Com. Palo Blanco, Salamanca 36885, Mexico)

Abstract

One of the earliest reports on synchronization of inert systems dates back to the time of the Dutch scientist Christiaan Huygens, who discovered that a pair of pendulum clocks coupled through a wooden bar oscillate in harmony. A remarkable feature in Huygens’ experiment is that different synchronous behaviors may be observed by just changing a parameter in the coupling. Motivated by this, in this paper, we propose a novel synchronization scheme for chaotic oscillators, in which the design of the coupling is inspired in Huygens’ experiment. It is demonstrated that the coupled oscillators may exhibit not only complete synchronization, but also mixed synchronization—some states synchronize in anti-phase whereas other states synchronize in-phase—depending on a single parameter of the coupling. Additionally, the stability of the synchronous solution is investigated by using the master stability function approach and the largest transverse Lyapunov exponent. The Lorenz system is considered as particular application example, and the performance of the proposed synchronization scheme is illustrated with computer simulations and validated by means of experiments using electronic circuits.

Suggested Citation

  • Jonatan Pena Ramirez & Adrian Arellano-Delgado & Rodrigo Méndez-Ramírez & Hector Javier Estrada-Garcia, 2024. "Synchronization of Chaotic Systems with Huygens-like Coupling," Mathematics, MDPI, vol. 12(20), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3177-:d:1496453
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    References listed on IDEAS

    as
    1. Blekhman, I.I. & Fradkov, A.L. & Tomchina, O.P. & Bogdanov, D.E., 2002. "Self-synchronization and controlled synchronization: general definition and example design," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 367-384.
    2. Márquez-Martínez, L.A. & Cuesta-García, J.R. & Pena Ramirez, J., 2022. "Boosting synchronization in chaotic systems: Combining past and present interactions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Jian Liu & Guanrong Chen & Xiu Zhao, 2021. "Generalized Synchronization And Parameters Identification Of Different-Dimensional Chaotic Systems In The Complex Field," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-13, June.
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