https://doi.org/10.1140/epjp/s13360-025-06849-1
Regular Article
Synchronization of the memristor-coupled memristive complex-valued FHN neurons
1
School of Mathematical Sciences, University of Jinan, 250022, Jinan, Shandong, China
2
School of Physics and Technology, University of Jinan, 250022, Jinan, Shandong, China
Received:
10
July
2025
Accepted:
10
September
2025
Published online:
25
September
2025
Complex-valued neurons can encode both amplitude and phase simultaneously, providing a biologically plausible way to model rich signal dynamics in real neural systems. Synaptic coupling is central to coordinating neuronal activity and transmitting information, and memristors—serving as synapse-like devices with internal memory—offer an effective mechanism for mediating its energy-based modulation. In this study, a sinusoidal flux-controlled memristor is used as a biological synapse to connect two memristive complex-valued FitzHugh-Nagumo (mCV-FHN) neurons, forming memristor-coupled mCV-FHN neurons (MC-mCV-FHNs), and their synchronization dynamics are investigated. The system has no equilibrium point and exhibits rich hidden dynamics, including hyperchaotic extreme multistability, multi-scroll attractors with scroll-growth, and pattern migration in firing activities. Based on Lyapunov stability theory in complex space, a rigorous and practical synchronization criterion is derived and numerically validated. The results show that complex synchronization transitions depend critically on both the memristor-coupling strength and the initial state of the memristive coupling channel. Additionally, the Hamilton energy of the mCV-FHN neuron is formulated using Helmholtz’s theorem, explaining the synchronization transition mechanism from an energy-balance perspective. This work establishes a foundation for scaling compact memristive neuron models to larger brain-inspired systems and offers a theoretical basis for future developments in neuromorphic computing and energy-efficient neural hardware.
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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.
