https://doi.org/10.1140/epjs/s11734-026-02129-w
Regular Article
Chaotic characteristics and stability analysis of a Hopfield neural network with a square hyperbolic tangent memristor
School of Engineering, Yanbian University, 133002, Yanji, China
a
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Received:
23
June
2025
Accepted:
7
January
2026
Published online:
14
January
2026
Neurons are the basic building blocks of the brain and possess the ability to generate a variety of complex dynamical behaviors. This paper proposes a hyperbolic tangent-type memristor for coupled neural networks, which consists of three neurons and a multistable memristive synapse. The effects of different coupling strengths on the dynamics of the neural network are analyzed using bifurcation diagrams, Lyapunov exponent spectra, and phase portraits. The study demonstrates that the Hopfield neural network exhibits rich dynamical behavior, including the coexistence of chaotic and periodic attractors, as well as hyper-multistability phenomena. Finally, to validate the feasibility and practical performance of the proposed system, the neural network was digitally implemented on an FPGA platform, confirming the significance of the theoretical analysis of the proposed HNN.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
