中国物理B ›› 2025, Vol. 34 ›› Issue (12): 120501-120501.doi: 10.1088/1674-1056/ae0a3b

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Discrete neuron models and memristive neural network mapping: A comprehensive review

Fei Yu(余飞)†, Xuqi Wang(王许奇), Rongyao Guo(郭荣垚), Zhijie Ying(应志杰), Yan He(何燕), and Qiong Zou(邹琼)   

  1. School of Physics and Electronics, Changsha University of Science and Technology, Changsha 410114, China
  • 收稿日期:2025-07-12 修回日期:2025-09-20 接受日期:2025-09-23 发布日期:2025-11-25
  • 通讯作者: Fei Yu E-mail:yufeiyfyf@csust.edu.cn
  • 基金资助:
    This work was supported by the Natural Science Foundation of Hunan Province (Grant No. 2025JJ50368), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 24A0248), and the Guiding Science and Technology Plan Project of Changsha City (Grant No. kzd2501129).

Discrete neuron models and memristive neural network mapping: A comprehensive review

Fei Yu(余飞)†, Xuqi Wang(王许奇), Rongyao Guo(郭荣垚), Zhijie Ying(应志杰), Yan He(何燕), and Qiong Zou(邹琼)   

  1. School of Physics and Electronics, Changsha University of Science and Technology, Changsha 410114, China
  • Received:2025-07-12 Revised:2025-09-20 Accepted:2025-09-23 Published:2025-11-25
  • Contact: Fei Yu E-mail:yufeiyfyf@csust.edu.cn
  • About author:2025-120501-251199.pdf
  • Supported by:
    This work was supported by the Natural Science Foundation of Hunan Province (Grant No. 2025JJ50368), the Scientific Research Fund of Hunan Provincial Education Department (Grant No. 24A0248), and the Guiding Science and Technology Plan Project of Changsha City (Grant No. kzd2501129).

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摘要： In recent years, discrete neuron and discrete neural network models have played an important role in the development of neural dynamics. This paper reviews the theoretical advantages of well-known discrete neuron models, some existing discretized continuous neuron models, and discrete neural networks in simulating complex neural dynamics. It places particular emphasis on the importance of memristors in the composition of neural networks, especially their unique memory and nonlinear characteristics. The integration of memristors into discrete neural networks, including Hopfield networks and their fractional-order variants, cellular neural networks and discrete neuron models has enabled the study and construction of various neural models with memory. These models exhibit complex dynamic behaviors, including superchaotic attractors, hidden attractors, multistability, and synchronization transitions. Furthermore, the present paper undertakes an analysis of more complex dynamical properties, including synchronization, speckle patterns, and chimera states in discrete coupled neural networks. This research provides new theoretical foundations and potential applications in the fields of brain-inspired computing, artificial intelligence, image encryption, and biological modeling.

关键词: discrete neuron, discrete neural network model, memristor, chaotic dynamics, memristive neural network

Abstract: In recent years, discrete neuron and discrete neural network models have played an important role in the development of neural dynamics. This paper reviews the theoretical advantages of well-known discrete neuron models, some existing discretized continuous neuron models, and discrete neural networks in simulating complex neural dynamics. It places particular emphasis on the importance of memristors in the composition of neural networks, especially their unique memory and nonlinear characteristics. The integration of memristors into discrete neural networks, including Hopfield networks and their fractional-order variants, cellular neural networks and discrete neuron models has enabled the study and construction of various neural models with memory. These models exhibit complex dynamic behaviors, including superchaotic attractors, hidden attractors, multistability, and synchronization transitions. Furthermore, the present paper undertakes an analysis of more complex dynamical properties, including synchronization, speckle patterns, and chimera states in discrete coupled neural networks. This research provides new theoretical foundations and potential applications in the fields of brain-inspired computing, artificial intelligence, image encryption, and biological modeling.

Key words: discrete neuron, discrete neural network model, memristor, chaotic dynamics, memristive neural network

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
07.05.Mh (Neural networks, fuzzy logic, artificial intelligence) 84.35.+i (Neural networks) 87.18.Sn (Neural networks and synaptic communication)