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Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model

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  • Mahmoud, Emad E.
  • Abo-Dahab, S.M.

Abstract

In this work, we present another chaotic (or hyperchaotic) complex nonlinear framework. This chaotic (or hyperchaotic) complex framework can be considered as a speculation of ”Guan” framework [1]. The new framework is a 5-dimensional nonstop real independent chaotic (or hyperchaotic) framework. The fundamental properties and elements of our framework are examined. Once with the all parameters are real and the other with one of these parameters is a complex parameter. When we examine the dynamics of the new framework and the parameters in real form, the conduct of the new framework is chaotic. While when one of these parameters is complex, our new framework is hyperchaotic. On the premise of Lyapunov capacity and dynamic control method, a scheme is designed to accomplish the complex anti-synchronization of two identical chaotic (or hyperchaotic) attractors of these frameworks. The effectiveness of the acquired outcomes will be delineated by a simulation case. Numerical outcomes are schemed to indicate state variables and errors of these chaotic attractors after synchronization to show that synchronization is accomplished. The above outcomes will give hypothetical establishment to the secure communication applications in light of the proposed scheme. In this secure communication scheme, synchronization between transmitter and receiver is accomplished and message signals will be recuperated. The encryption and rebuilding of the signals will be simulated numerically.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:106:y:2018:i:c:p:273-284
    DOI: 10.1016/j.chaos.2017.10.013
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    References listed on IDEAS

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    1. Gamal M. Mahmoud & Mansour E. Ahmed & Emad E. Mahmoud, 2008. "Analysis Of Hyperchaotic Complex Lorenz Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(10), pages 1477-1494.
    2. Yan, Zhenya & Yu, Pei, 2008. "Hyperchaos synchronization and control on a new hyperchaotic attractor," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 333-345.
    3. 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.
    4. 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.
    5. Álvarez, G. & Li, Shujun & Montoya, F. & Pastor, G. & Romera, M., 2005. "Breaking projective chaos synchronization secure communication using filtering and generalized synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 775-783.
    6. Bai, Er-Wei & Lonngren, Karl E. & Uçar, Ahmet, 2005. "Secure communication via multiple parameter modulation in a delayed chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1071-1076.
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    Cited by:

    1. Emad E. Mahmoud & M. Higazy & Turkiah M. Al-Harthi, 2019. "A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Applicatio," Mathematics, MDPI, vol. 7(10), pages 1-26, September.
    2. J. Humberto Pérez-Cruz, 2018. "Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control," Complexity, Hindawi, vol. 2018, pages 1-19, December.
    3. Mahmoud, Gamal M. & Mahmoud, Emad E. & Arafa, Ayman A., 2018. "Synchronization of time delay systems with non-diagonal complex scaling functions," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 86-95.
    4. Jiaxun Liu & Zuoxun Wang & Minglei Shu & Fangfang Zhang & Sen Leng & Xiaohui Sun, 2019. "Secure Communication of Fractional Complex Chaotic Systems Based on Fractional Difference Function Synchronization," Complexity, Hindawi, vol. 2019, pages 1-10, August.
    5. Hao, Zhang & Xing-yuan, Wang & Peng-fei, Yan & Yu-jie, Sun, 2020. "Combination synchronization and stability analysis of time-varying complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Fangfang Zhang & Rui Gao & Zhe Huang & Cuimei Jiang & Yawen Chen & Haibo Zhang, 2022. "Complex Modified Projective Difference Function Synchronization of Coupled Complex Chaotic Systems for Secure Communication in WSNs," Mathematics, MDPI, vol. 10(7), pages 1-14, April.
    7. 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).
    8. Zuoxun Wang & Wenzhu Zhang & Lei Ma & Guijuan Wang, 2022. "Several Control Problems of a Class of Complex Nonlinear Systems Based on UDE," Mathematics, MDPI, vol. 10(8), pages 1-15, April.

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