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Open Access

ARTICLE

A Dual-Neuron Memristor Hopfield Neural Network with Controllable Multiple Equilibrium Points: Dynamical Analysis, FPGA Implementation, and Image Encryption Application

Yanyu Zhu1, Jie Jin2,*, Lv Zhao2,3, Fei Yu4
1 School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China
2 School of Information Engineering, Changsha Medical University, Changsha, China
3 School of Electrical and Information Engineering, Hunan Institute of Technology, Hengyang, China
4 School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China
* Corresponding Author: Jie Jin. Email: email
(This article belongs to the Special Issue: Applied Cryptography and Privacy-Enhancing Technologies for Secure Digital Infrastructures)

Computers, Materials & Continua https://doi.org/10.32604/cmc.2026.085516

Received 12 May 2026; Accepted 27 July 2026; Published online 24 August 2026

Abstract

To address the issues of multi-neuron architectures, high parameter redundancy, and complex hardware implementation in existing memristive Hopfield neural networks (MHNN) for image encryption, a simple structure dual-neuron memristive Hopfield neural network (DNMHNN) modulated by multifrequency square waves is proposed in this study. The proposed DNMHNN model consists of only two neurons and one memristor, and by introducing dual-frequency square-wave external excitation into the memristor, the dynamical behavior of the DNMHNN model can be flexibly regulated. The simulation results verify that the proposed DNMHNN model can generate stable chaotic behavior over a wide parameter range. Furthermore, the DNMHNN is also implemented on a Zynq-7000 FPGA platform, and the experimental results are highly consistent with the numerical simulations, demonstrating the feasibility and stability of the DNMHNN model in practical hardware applications. On this basis, a DNMHNN-based image encryption algorithm with pixel permutation, XOR substitution, and bidirectional ciphertext-feedback diffusion is designed using chaotic sequences generated by the DNMHNN model. Security analysis indicates that the DNMHNN-based image encryption algorithm exhibits strong performance in histogram distribution, correlation reduction, information entropy, NPCR, UACI, key sensitivity, and resistance to noise, occlusion, tampering, and differential attacks, which is further verified by quantitative robustness metrics including MSE, PSNR, SSIM, and recovered-image correlation. The results demonstrate that the proposed dual-neuron memristive DNMHNN maintains a simple structure while preserving rich chaotic dynamical properties. Therefore, it provides an effective chaotic key source for lightweight image encryption and edge secure computing.

Keywords

Memristor; Hopfield neural network (HNN); chaotic dynamics; FPGA implementation; image encryption

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