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Modified generalized projective synchronization of the geomagnetic Krause and Robert fractional-order chaotic system and its application in secure communication

Author

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  • Haneche Nabil

    (University of Mentouri Brothers)

  • Hamaizia Tayeb

    (University of Mentouri Brothers)

Abstract

In recent years, a significant deal of interest has been observed in the applications of chaotic systems in physics and chemistry. In chaos theory, when a nonlinear dynamical system has at least one positive Lyapunov exponent, it is said to be chaotic. This paper is concerned with the investigation of chaotic dynamics of the geomagnetic Krause and Robert fractional-order system (1981), which is based on the Rikitake two-disc dynamical system. The numerical solution of the fractional-order system is derived by adopting the Adomian decomposition method (ADM). The chaotic behavior of the system is investigated via powerful nonlinear tools. In addition, the level of complexity in the fractional-order system is quantified via $$C_{0}$$ C 0 complexity and spectral entropy algorithms. Furthermore, a chaos synchronization via modified generalized projective synchronization (MGPS) of the fractional-order system is achieved. Thus, MGPS of the fractional-order system is applied to secure communication. Graphic Abstract

Suggested Citation

  • Haneche Nabil & Hamaizia Tayeb, 2025. "Modified generalized projective synchronization of the geomagnetic Krause and Robert fractional-order chaotic system and its application in secure communication," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(4), pages 1-19, April.
    • Handle: RePEc:spr:eurphb:v:98:y:2025:i:4:d:10.1140_epjb_s10051-025-00897-3
    DOI: 10.1140/epjb/s10051-025-00897-3
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    References listed on IDEAS

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    1. Liang Chen & Chengdai Huang & Haidong Liu & Yonghui Xia, 2019. "Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order," Mathematics, MDPI, vol. 7(6), pages 1-16, June.
    2. Junbiao Guan & Kaihua Wang, 2015. "Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, February.
    3. Hong-Juan Liu & Zhi-Liang Zhu & Hai Yu & Qian Zhu, 2013. "Modified Function Projective Synchronization of Fractional Order Chaotic Systems with Different Dimensions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, November.
    4. Du, Hongyue & Zeng, Qingshuang & Wang, Changhong, 2009. "Modified function projective synchronization of chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2399-2404.
    5. Li, Guo-Hui, 2007. "Modified projective synchronization of chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1786-1790.
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