Fixed points as regulatory hubs in discrete memristive neural networks: An analysis of the FitzHugh-Nagumo model

doi:10.1088/1674-1056/ae3131

Abstract This study investigates the dynamics of discrete memristive FitzHugh-Nagumo (FHN) neural networks. We introduce a discrete memristor with hyperbolic tangent nonlinearity and incorporate it into neuron models ranging from single neurons and coupled pairs to complex networks with ring and small-world topologies. Stability and bifurcation analyses reveal transitions from periodic to chaotic dynamics. A key contribution is the identification of a constant fixed point that remains invariant across periodic, weakly chaotic, and chaotic regimes. Linear stability analysis of this fixed point provides a fundamental basis for understanding the system's dynamical evolution. The fixed point theory explains how memristive coupling induces diverse synchronization patterns, including stable phase-locking and synchronization-desynchronization transitions, and further accounts for the emergence of chimera states in ring networks as well as their alteration in small-world networks owing to long-range connections. Field-programmable gate array (FPGA) implementation successfully validates the mathematical models, confirming the feasibility of hardware realization. Overall, this work establishes a theoretical framework linking fixed point properties with firing mechanisms and synchronization dynamics in discrete memristive FHN neural networks, providing insights into potential applications in neuromorphic computing.

Keywords: discrete memristor discrete neuron complex network chimera state FPGA implementation

Received: 29 September 2025
Revised: 24 December 2025
Accepted manuscript online: 26 December 2025

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	84.30.-r	(Electronic circuits)
	89.75.-k	(Complex systems)
	07.05.-t	(Computers in experimental physics)

Fund: This project was supported by the Natural Science Foundation of China (Grant Nos. 62501516, 61901530, 62071496, and 62061008), the Natural Science Foundation of Hunan Province (Grant No. 2020JJ5767), and the Natural Science Foundation of Hunan Province (Grant No. 2025JJ50391).

Corresponding Authors: Qilai Chen
E-mail: chenqilai277@xtu.edu.cn

Cite this article:

Shaobo He(贺少波), Jiawei Xiao(肖佳伟), Qilai Chen(陈祺来), and Huihai Wang(王会海) Fixed points as regulatory hubs in discrete memristive neural networks: An analysis of the FitzHugh-Nagumo model 2026 Chin. Phys. B 35 060502

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Fixed points as regulatory hubs in discrete memristive neural networks: An analysis of the FitzHugh-Nagumo model

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