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Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints

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  • Min, Fuhong
  • Luo, Albert C.J.

Abstract

In this paper, periodic and chaotic synchronizations between two distinct dynamical systems under specific constraints are investigated from the theory of discontinuous dynamical systems. The analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator were obtained, and the invariant domain of sinusoidal synchronization is achieved. From analytical conditions, the control parameter map is developed. Numerical illustrations for partial and full sinusoidal synchronizations of chaotic and periodic motions of the controlled pendulum with the Duffing oscillator are carried out. This paper presents how to apply the theory of discontinuous dynamical systems to dynamical system synchronization with specific constraints. The function synchronization of two distinct dynamical systems with specific constraints should be identified only by G-functions. The significance of function synchronization of distinct dynamical systems is to make the synchronicity behaviors hidden, which is very useful for telecommunication synchronization and network security.

Suggested Citation

  • Min, Fuhong & Luo, Albert C.J., 2012. "Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 998-1011.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:7:p:998-1011
    DOI: 10.1016/j.chaos.2012.03.012
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    References listed on IDEAS

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    1. N. Fujiwara & J. Kurths, 2009. "Spectral universality of phase synchronization in non-identical oscillator networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 45-49, May.
    2. Park, Ju H., 2005. "Stability criterion for synchronization of linearly coupled unified chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1319-1325.
    3. Luo, Albert C.J. & Min, Fuhong, 2011. "Synchronization dynamics of two different dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 362-380.
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    Cited by:

    1. Wang, Ran & Li, Chunbiao & Kong, Sixiao & Jiang, Yicheng & Lei, Tengfei, 2022. "A 3D memristive chaotic system with conditional symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Liang, Bo & Hu, Chenyang & Tian, Zean & Wang, Qiao & Jian, Canling, 2023. "A 3D chaotic system with multi-transient behavior and its application in image encryption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).

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