https://doi.org/10.1140/epjp/s13360-025-06953-2
Regular Article
A memristive hyperchaotic map with extreme multistability: dynamics, complexity, and application in image encryption
1
Applied Mathematics and Modeling Laboratory, University of Mentouri Brothers, Constantine, Algeria
2
Mathematical Modeling and Simulation Laboratory, University of Mentouri Brothers, Constantine, Algeria
a
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Received:
31
August
2025
Accepted:
8
October
2025
Published online:
18
October
2025
Abstract
The memristor’s capacity to change its resistive state in response to external stimuli allows it to serve as the foundation for generating pseudorandom sequences via appropriate control circuitry. Capitalizing on this property, we present a three-dimensional memristive hyperchaotic map (3D-MHM), formulated by merging a sinusoidal nonlinearity with a discrete memristor model to amplify chaotic complexity. An investigation of its dynamics through Lyapunov exponents reveals that the 3D-MHM undergoes transitions from periodic states to chaos and hyperchaos. The intricacy of its iterative output is further validated using metrics such as permutation entropy and 
complexity. A distinctive analysis of this system reveals that it can produce coexisting attractors and multistability, where varying the initial conditions leads to attractors appearing at different spatial positions. Furthermore, the offset boosting behavior of the 3D-MHM displays the coexistence of an infinite number of homogeneous attractors boosted by the memristor initial condition. Leveraging these attributes, a novel color image encryption algorithm based on the 3D-MHM is proposed, presenting a more secure scheme for large-volume data encryption. Statistical and cryptographic analyses confirm the significant potential of the keystream produced by the 3D-MHM for cryptographic applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica 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.
