https://doi.org/10.1140/epjb/s10051-025-00897-3
Regular Article - Statistical and Nonlinear Physics
Modified generalized projective synchronization of the geomagnetic Krause and Robert fractional-order chaotic system and its application in secure communication
1
Applied Mathematics and Modeling Laboratory, Department of Mathematics, University of Mentouri Brothers, 25000, Constantine, Algeria
2
Mathematical Modeling and Simulation Laboratory, Department of Mathematics, University of Mentouri Brothers, 25000, Constantine, Algeria
a
nabil.haneche@doc.umc.edu.dz
Received:
20
July
2024
Accepted:
6
March
2025
Published online:
7
April
2025
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 
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.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
