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A hyperchaotic detuned laser model with an infinite number of equilibria existing on a plane and its modified complex phase synchronization with time lag

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  • Mahmoud, Emad E.
  • AL-Harthi, Bushra H.

Abstract

The objective of this research is to implement a contemporary hyperchaotic complex detuned laser system. Here, the hyperchaotic complex system is developed by combining a straight controller to the chaotic complex detuned laser system. The new system is a seven-dimensional real continuous autonomous hyperchaotic system. This system’s characteristics, including the Hamiltonian, dissipative, fixed points and its stability, Lyapunov dimension, Lyapunov exponents, and bifurcation diagrams are examined, as is the achievement of hyperchaos. Different forms of hyperchaotic complex detuned laser systems are constructed. Additionally, we present another type of synchronization for complex nonlinear systems only, termed modified complex phase synchronization with a time lag (MCPSTL). Given Lyapunov stability, the aim is to achieve MCPSTL of two indistinguishable hyperchaotic trajectories of these systems. A simulation is performed to demonstrate the viability of this approach. Numerical methods are used to calculate the variable and error states of these hyperchaotic trajectories after synchronization. The results provide a theoretical foundation for applications of the proposed approach in secure communication. Signal encryption and alteration are conducted numerically.

Suggested Citation

  • Mahmoud, Emad E. & AL-Harthi, Bushra H., 2020. "A hyperchaotic detuned laser model with an infinite number of equilibria existing on a plane and its modified complex phase synchronization with time lag," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303881
    DOI: 10.1016/j.chaos.2019.109442
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    References listed on IDEAS

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    1. Emad E. Mahmoud & Fatimah S. Abood, 2017. "A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization," Complexity, Hindawi, vol. 2017, pages 1-13, August.
    2. Mahmoud, Emad E., 2013. "Modified projective phase synchronization of chaotic complex nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 69-85.
    3. Mahmoud, Emad E. & Abo-Dahab, S.M., 2018. "Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 273-284.
    4. Vafamand, Navid & Khorshidi, Shapour & Khayatian, Alireza, 2018. "Secure communication for non-ideal channel via robust TS fuzzy observer-based hyperchaotic synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 116-124.
    5. Li, Guo-Hui, 2007. "Modified projective synchronization of chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1786-1790.
    6. Mahmoud, Gamal M. & Mahmoud, Emad E., 2010. "Synchronization and control of hyperchaotic complex Lorenz system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2286-2296.
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    Cited by:

    1. Li, Xuejun & Mou, Jun & Banerjee, Santo & Wang, Zhisen & Cao, Yinghong, 2022. "Design and DSP implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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