Memristor-coupled dynamics and synchronization in two bi-neuron Hopfield neural networks

doi:10.1088/1674-1056/ae101c

Abstract Neural synchronization is associated with various brain disorders, making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks. In this paper, we propose a minimal architecture as a prototype, consisting of two bi-neuron Hopfield neural networks (HNNs) coupled via a memristor. This coupling elevates the original two bi-neuron HNNs into a five-dimensional system, featuring an unstable line equilibrium set and rich dynamics absent in the uncoupled case. Our results show that varying the coupling strength and the initial state of the memristor can induce periodic, chaotic, hyperchaotic, and quasi-periodic oscillations, as well as initial-offset-regulated multistability. We derive sufficient conditions for achieving exponential synchronization and identify multiple synchronous regimes with transitions that strongly depend on the initial states. Field-programmable gate array (FPGA) implementation confirms the predicted dynamics and synchronization in real time, demonstrating that the memristive coupler enables complex dynamics and controllable synchronization in the most compact Hopfield architecture, with implications for the study of neuromorphic circuits and synchronization.

Keywords: memristor bi-neuron Hopfield neural network (HNN) initial state dependence synchronization

Received: 18 August 2025
Revised: 03 October 2025
Accepted manuscript online: 07 October 2025

PACS:	87.19.lg	(Synapses: chemical and electrical (gap junctions))
	87.19.lj	(Neuronal network dynamics)
	87.19.lm	(Synchronization in the nervous system)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 62271088), the Qinglan Project of Jiangsu Province, and the Jiangsu Government Scholarship for Overseas Studies, the Training Plan of Young Backbone Teachers in Universities of Henan Province (Grant No. 2023GGJS142), and the Key Scientific Research of Colleges and Universities in Henan Province (Grant No. 25A120009).

Corresponding Authors: Bocheng Bao
E-mail: mervinbao@126.com

Cite this article:

Fangyuan Li(李芳苑), Haigang Tang(唐海刚), Yunzhen Zhang(张云贞), Bocheng Bao(包伯成), Hany Hassanin, and Lianfa Bai(柏连发) Memristor-coupled dynamics and synchronization in two bi-neuron Hopfield neural networks 2025 Chin. Phys. B 34 128701

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Memristor-coupled dynamics and synchronization in two bi-neuron Hopfield neural networks

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