https://doi.org/10.1140/epjs/s11734-025-01784-9
Regular Article
A Sigmoid-type memristor and its application in Hopfield neural network
1
School of Information Engineering, Xuchang University, 461000, Xuchang, China
2
School of Information and Control Engineering, Jilin Institute of Chemical Technology, 132022, Jilin, China
3
School of Electrical and Information Engineering, Jiangsu University of Technology, 213001, Changzhou, China
Received:
16
April
2025
Accepted:
27
June
2025
Published online:
9
July
2025
The Sigmoid function is a smooth and differentiable positive threshold function, which exhibits a typical ‘S’-shaped nonlinear characteristic. This paper proposes an innovative Sigmoid-type memristor emulator that uses Sigmoid function as memductance function. The pinched hysteresis loop characteristics are systematically analyzed through numerical measurements and validated by circuit simulation. This emulator has enabled the development of a new Sigmoid-type memristive Hopfield neural network (Sigmoid-MHNN). The Sigmoid-MHNN exhibits a line equilibrium point, and its stability is always unstable for different coupling strength and memristor initial value. Through comprehensive numerical analyses including dual-parameter bifurcation diagram, one-dimensional bifurcation diagrams, Lyapunov exponent spectra, attraction basin, and phase portraits, we confirm that the proposed Sigmoid-MHNN manifests complex dynamical behaviors ranging from spiral and double-scroll chaotic attractors with different topologies, limit cycles with different number of periods and different phase space, and so on. Notably, the system also exhibits extreme multistability where infinite attractors coexist depending on memristor and non-memristor initial values. Finally, analog circuit implementations successfully corroborate the physical realizability of these complex dynamics.
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© The Author(s), under exclusive licence to EDP Sciences, 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.
