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Modified projective phase synchronization of chaotic complex nonlinear systems

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  • Mahmoud, Emad E.

Abstract

This paper introduces the concept of Modified Projective Phase Synchronization (MPPS) for interacting chaotic systems with complex variables. The idea is that the number of effective state variables can be increased by treating the real and imaginary parts separately. On the basis of the Lyapunov stability theory, a scheme is designed to realize the new form of chaotic synchronization, and we demonstrate how chaotic complex systems in a master–slave configuration can be synchronized to a constant scaling matrix. The speed and accuracy of the synchronization are illustrated by means of computer simulation.

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  • 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.
    • Handle: RePEc:eee:matcom:v:89:y:2013:i:c:p:69-85
    DOI: 10.1016/j.matcom.2013.02.008
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    References listed on IDEAS

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    1. Li, Guo-Hui, 2007. "Generalized projective synchronization between Lorenz system and Chen’s system," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1454-1458.
    2. GAMAL M. MAHMOUD & M. A. Al-KASHIF & SHABAN A. ALY, 2007. "Basic Properties And Chaotic Synchronization Of Complex Lorenz System," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 253-265.
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    4. 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.
    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. 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. 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.
    3. 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).
    4. Xuan-Toa Tran & Hee-Jun Kang, 2017. "Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems," Complexity, Hindawi, vol. 2017, pages 1-9, July.
    5. Wu, Xiangjun & Zhu, Changjiang & Kan, Haibin, 2015. "An improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 201-214.
    6. Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    7. 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.
    8. 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.
    9. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    10. 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.
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    13. Cuimei Jiang & Shutang Liu, 2017. "Synchronization and Antisynchronization of -Coupled Complex Permanent Magnet Synchronous Motor Systems with Ring Connection," Complexity, Hindawi, vol. 2017, pages 1-15, January.

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