中国物理B ›› 2025, Vol. 34 ›› Issue (12): 128701-128701.doi: 10.1088/1674-1056/ae101c

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

Fangyuan Li(李芳苑)1,2, Haigang Tang(唐海刚)3, Yunzhen Zhang(张云贞)4, Bocheng Bao(包伯成)3,†, Hany Hassanin5, and Lianfa Bai(柏连发)2   

  1. 1 School of Electronic Information, Nanjing Vocational College of Information Technology, Nanjing 210023, China;
    2 School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;
    3 Wang Zheng School of Microelectronics, Changzhou University, Changzhou 213159, China;
    4 School of Information Engineering, Xuchang University, Xuchang 461000, China;
    5 School of Engineering, Technology and Design, Canterbury Christ Church University, Canterbury CT11QU, UK
  • 收稿日期:2025-08-18 修回日期:2025-10-03 接受日期:2025-10-07 发布日期:2025-12-04
  • 通讯作者: Bocheng Bao E-mail:mervinbao@126.com
  • 基金资助:
    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).

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

Fangyuan Li(李芳苑)1,2, Haigang Tang(唐海刚)3, Yunzhen Zhang(张云贞)4, Bocheng Bao(包伯成)3,†, Hany Hassanin5, and Lianfa Bai(柏连发)2   

  1. 1 School of Electronic Information, Nanjing Vocational College of Information Technology, Nanjing 210023, China;
    2 School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;
    3 Wang Zheng School of Microelectronics, Changzhou University, Changzhou 213159, China;
    4 School of Information Engineering, Xuchang University, Xuchang 461000, China;
    5 School of Engineering, Technology and Design, Canterbury Christ Church University, Canterbury CT11QU, UK
  • Received:2025-08-18 Revised:2025-10-03 Accepted:2025-10-07 Published:2025-12-04
  • Contact: Bocheng Bao E-mail:mervinbao@126.com
  • Supported by:
    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).

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摘要： 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.

关键词: memristor, bi-neuron Hopfield neural network (HNN), initial state dependence, synchronization

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.

Key words: memristor, bi-neuron Hopfield neural network (HNN), initial state dependence, synchronization

中图分类号:  (Synapses: chemical and electrical (gap junctions))

  • 87.19.lg
87.19.lj (Neuronal network dynamics) 87.19.lm (Synchronization in the nervous system) 05.45.-a (Nonlinear dynamics and chaos)