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

Haneche Nabil () and Hamaizia Tayeb ()
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Haneche Nabil: University of Mentouri Brothers
Hamaizia Tayeb: University of Mentouri Brothers

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 4, 1-19

Abstract: 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

Date: 2025
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DOI: 10.1140/epjb/s10051-025-00897-3

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