https://doi.org/10.1140/epjs/s11734-025-01989-y
Regular Article
Complex dynamics and synchronization of a memristive membrane neuron model with bounded hyperbolic memductance
1
Center for Research, Easwari Engineering College, Chennai, India
2
Center for Research, SRM TRP Engineering College, Trichy, India
3
Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, Trichy, India
4
School of Mathematics and Physics, China University of Geosciences, 430074, Wuhan, China
5
University of Wisconsin, 1150 University Avenue, 53706-1390, Madison, WI, USA
a
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Received:
19
July
2025
Accepted:
23
September
2025
Published online:
12
October
2025
Abstract
The membrane potential of a neuron, driven by ionic concentration gradients and electromagnetic fields, can be equivalently modeled with a double-membrane capacitive system connected by a memristor, effectively capturing the flexible and controllable electrical characteristics of biological membranes. In this work, we propose a novel memristive membrane neuron model featuring a tangent hyperbolic memductance, which introduces a biologically plausible, bounded, and saturating nonlinearity. This model exhibits a rich variety of dynamic behaviors, including periodic spiking, chaotic firing, and multistability, where multiple distinct firing patterns coexist under identical parameters. Under external periodic excitation, the model exhibits extreme events, characterized by rare and abnormally large spikes, mimicking pathological neuronal activity. We further define and analyze the system’s energy function, demonstrating its utility in understanding internal dynamics and informing coupling strategies in neural networks. When organized in a small-world topology, the network of coupled neurons not only achieves synchronization but also reveals the emergence of diverse partially synchronized states, where coherent and incoherent activity coexist. These findings position the proposed model as a powerful tool for exploring both healthy and abnormal neural behaviors at the single-neuron and network levels.
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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.
