| TOPICAL REVIEW — Biophysical circuits: Modeling & applications in neuroscience |
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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) |
| School of Physics and Electronics, Changsha University of Science and Technology, Changsha 410114, China |
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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.
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Received: 12 July 2025
Revised: 20 September 2025
Accepted manuscript online: 23 September 2025
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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07.05.Mh
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(Neural networks, fuzzy logic, artificial intelligence)
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84.35.+i
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(Neural networks)
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87.18.Sn
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(Neural networks and synaptic communication)
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| Fund: 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). |
Corresponding Authors:
Fei Yu
E-mail: yufeiyfyf@csust.edu.cn
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| About author: 2025-120501-251199.pdf |
Cite this article:
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) Discrete neuron models and memristive neural network mapping: A comprehensive review 2025 Chin. Phys. B 34 120501
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[1] Zhang Z, He Y, MaiW, Luo Y, Li X, Cheng Y, Huang X and Lin R 2024 IEEE Transactions on Neural Networks and Learning Systems 1-12
[2] Ma J and Tang J 2017 Nonlinear Dyn. 89 1569
[3] Li T, Wang G, Yu D, Ding Q and Jia Y 2022 Nonlinear Dyn. 108 2611
[4] Hua C, Cao X and Liao B 2025 Computational Intelligence 41 e70042
[5] Hodgkin A L and Huxley A F 1990 Bulletin of Mathematical Biology 52 25
[6] Morris C and Lecar H 1981 Biophysical Journal 35 193
[7] Hindmarsh J L and Rose R M 1982 Nature 296 162
[8] Chay T R 1985 Physica D 16 233
[9] Shilnikov A L and Rulkov N F 2004 Phys. Lett. A 328 177
[10] Aguirre C, Campos D, Pascual P and Serrano E 2005 A model of spiking-bursting neuronal behavior using a piecewise linear twodimensional map Ed. by Cabestany J, Prieto A and Sandoval F (Berlin, Heidelberg: Springer Berlin Heidelberg) pp. 130-135
[11] Rulkov N F 2001 Phys. Rev. Lett. 86 183
[12] Chialvo D R 1995 Chaos, Solitons & Fractals 5 461
[13] Izhikevich E M and Hoppensteadt F 2004 International Journal of Bifurcation and Chaos 14 3847
[14] Courbage M, Nekorkin V I and Vdovin L V 2007 Chaos 17 043109
[15] Deng Q, Wang C, Sun Y and Yang G 2025 Nonlinear Dyn. 113 17161
[16] Deng Q,Wang C, Sun Y, Cong X, Lin H and Deng Z 2025 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 1-1
[17] Wang C, Li Y, Yang G and Deng Q 2025 Mathematics 13 1600
[18] Duan Z, Zhang X, He S, Yu X, Xiong P, Chen J and Wang Q 2024 Integration 99 102258
[19] Zhao Y, Ding J, He S, Wang H and Sun K 2023 AEU - International Journal of Electronics and Communications 161 154522
[20] Rong X, Chedjou J C, Yu X, Shukhratovich M B, Jiang D and Kengne J 2024 Chaos, Solitons & Fractals 189 115704
[21] Shen Y, Chen Z, Li Y and Li W 2025 Mechanical Systems and Signal Processing 229 112525
[22] Dong Y, Yang S, Liang Y andWang G 2022 Chaos, Solitons & Fractals 160 112241
[23] Huang L, Jin P, Zang H, Fu H, Lei T andWang G 2025 Chaos, Solitons & Fractals 195 116271
[24] Luo D, Wang C, Deng Q and Yang G 2025 Nonlinear Dyn. pp. 1-15
[25] Luo Y, Li X, Li Z, Xie J, Zhang Z and Li X 2024 IEEE Transactions on Cybernetics 54 5866
[26] Deng Q, Wang C, Sun Y and Yang G 2025 IEEE Transactions on Circuits and Systems I: Regular Papers pp. 1-11
[27] Dong Y, Wang G, Chen G, Shen Y and Ying J 2020 Communications in Nonlinear Science and Numerical Simulation 84 105203
[28] Liang Y, Wang G, Chen G, Dong Y, Yu D and Iu H H C 2020 IEEE Transactions on Circuits and Systems I: Regular Papers 67 5139
[29] Gu W Y, Wang G Y, Dong Y J and Ying J J 2020 Chin. Phys. B 29 110503
[30] Tan Y and Wang C 2020 Chaos 30 053118
[31] Xin Y, Zhang J, Cheng Z and Cao J 2025 Communications in Nonlinear Science and Numerical Simulation 148 108857
[32] He T, Yu F, Lin Y, He S, Yao W, Cai S and Jin J 2025 Chin. Phys. B 34 120506
[33] Wan Q, Chen S, Liu T, Lan H and Shen K 2025 Integration 103 102410
[34] Ding S, Lin H, Deng X, Yao W and Jin J 2025 Expert Systems with Applications 277 127168
[35] Zhang H, Yan S and Zhang Y 2025 Neurocomputing 645 130540
[36] Yu F, Gracia Y M, Guo R, Ying Z, Xu J, Yao W, Jin J and Lin H 2025 Axioms 14 638
[37] Zhu J, Jin J, Chen C, Wu L, Lu M and Ouyang A 2025 IEEE Transactions on Emerging Topics in Computational Intelligence 9 176
[38] Yu F,Wu C, Xu S, YaoW, Xu C, Cai S andWang C 2025 Signal, Image and Video Processing 19 77
[39] Fan C and Ding Q 2025 Chaos, Solitons & Fractals 191 115905
[40] Yu F, Xu S, Xiao X, Yao W, Huang Y, Cai S and Li Y 2024 Integration 96 102129
[41] Yang L and Lai Q 2024 Integration 94 102091
[42] He S, Yu F, Guo R, Zheng M, Tang T, Jin J and Wang C 2025 Fractal and Fractional 9 561
[43] Yu F, Kong X, Yao W, Zhang J, Cai S, Lin H and Jin J 2024 Chaos, Solitons & Fractals 179 114440
[44] Chen Y, Lai Q, Zhang Y, Erkan U and Toktas A 2024 Nonlinear Dyn. 112 8603
[45] Yu F, Lin Y, Yao W, Cai S, Lin H and Li Y 2025 Neural Networks 182 106904
[46] Lu J, Min F, Gan L and Zhu W 2025 Nonlinear Dyn. 113 21951
[47] Deng Q,Wang C and Yang G 2025 International Journal of Bifurcation and Chaos 35 2550053
[48] Luo D W, Wang C H, Liang J H and Deng Q L 2025 Nonlinear Dyn. 113 29983
[49] Jin J, Chen W, Ouyang A, Yu F and Liu H 2024 IEEE Transactions on Emerging Topics in Computational Intelligence 8 364
[50] Lai Q and Chen Y 2024 Chaos, Solitons & Fractals 187 115473
[51] Xie Y and Lai Q 2024 Integration 97 102196
[52] Lai Q and Guo S 2024 Neural Networks 178 106412
[53] Tang Z and Zhang Y 2023 Neurocomputing 561 126883
[54] Yu F, He S, Yao W, Cai S and Xu Q 2025 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 1-1
[55] Yu F, Su D, He S, Wu Y, Zhang S and Yin H 2025 Chin. Phys. B 34 050502
[56] Xiao P, Fang J, Wei Z, Dong Y, Du S, Wen S and Hong Q 2025 IEEE Transactions on Automation Science and Engineering 22 15163
[57] Lai Q and Yang L 2023 Chaos, Solitons & Fractals 174 113807
[58] Al-Husban A, Karoun R C, Heilat A S, Horani M A, Khennaoui A A, Grassi G, Radogna A V and Ouannas A 2023 Alexandria Engineering Journal 75 627
[59] Ma W, Li X, Yu T and Wang Z 2023 Optik 291 171387
[60] Peng Y, Li M, Li Z, Ma M, Wang M and He S 2025 Neural Networks 185 107213
[61] Xiang Q, Gong H and Hua C 2025 The Journal of Supercomputing 81 1
[62] He S, Liu J, Wang H and Sun K 2023 Neurocomputing 523 1
[63] Li H and Min F 2024 IEEE Transactions on Industrial Informatics 20 10259
[64] Wei Y, Du B,Wang X, Fan Z and Sun X 2025 Nonlinear Dyn. 113 2729
[65] Lai Q, Zhu C, Qin M and Wan Z 2025 Mathematics and Computers in Simulation 236 270
[66] Chua L 1971 IEEE Transactions on Circuit Theory 18 507
[67] Strukov D B, Snider G S, Stewart D R and Williams R S 2008 Nature 453 80
[68] Boya B F B A, Kengne J, Nanfak A, Muni S S, de Dieu Nkapkop J, Kenmoe G D and Babenko L K 2025 Franklin Open 10 100210
[69] Zhang S, Yao W, Xiong L, Wang Y, Tang L, Zhang X and Yu F 2024 Chaos, Solitons & Fractals 187 115408
[70] Li F, QinW, Xi M, Bai L and Bao B 2025 Neural Networks 183 107049
[71] Negrov D, Karandashev I, Shakirov V, Matveyev Y, Dunin-Barkowski W and Zenkevich A 2017 Neurocomputing 237 193
[72] Shi F, Cao Y, Banerjee S, Ahmad AMand Mou J 2024 Chaos, Solitons & Fractals 189 115723
[73] Wang C, Li Y and Deng Q 2025 Chaos, Solitons & Fractals 193 116053
[74] Yu F, Tan B, He T, He S, Huang Y, Cai S and Lin H 2025 Mathematics 13 726
[75] Jin J,Wu M, Ouyang A, Li K and Chen C 2025 IEEE Internet of Things Journal 12 14297
[76] Guo Y, Zhang J, Xie Q and Hou J 2023 Optik 287 171119
[77] Luo C, Bao H and Cao J 2025 Journal of the Franklin Institute 362 107552
[78] Zhang C,Wang H and Zhang Y 2025 Expert Systems with Applications 286 128091
[79] Deng Q L, Wang C H, Sun Y C and Yang G 2025 IEEE Transactions on Cybernetics 55 3926
[80] Kuznetsov A, Sedova Y and Stankevich N 2024 Chaos, Solitons & Fractals 186 115237
[81] Xu Q, Huang L and Wang Huagan Chen M 2023 Nonlinear Dyn. 111 20447
[82] Huang L, Fan W, Feng C, Bao H, Wang N and Xu Q 2025 AEU - International Journal of Electronics and Communications 189 155597
[83] Wagemakers A and Sanjuan M A F 2013 Journal of the Franklin Institute 350 2901
[84] Bashkirtseva I, Nasyrova V and Ryashko L 2018 Chaos, Solitons & Fractals 110 76
[85] Hu B, Li D and Hou H 2016 Journal of Taiyuan University of Technology 47 552
[86] Muni S S, Rajagopal K, Karthikeyan A and Arun S 2022 Chaos, Solitons & Fractals 155 111759
[87] Sou N, Haruhiko N, Teruya Y, Liu J Q and Gennady C 2015 Plos One 10 e0138919
[88] Andabili M N, Nazari S and Moosazadeh T 2025 Scientific Reports 15 16766
[89] Zhu W, Sun K, Wang H, Fu L and Minati L 2024 Chaos, Solitons & Fractals 186 115281
[90] Hongjun J, Jiang W, Haitao Y, Bin D and Xile W 2011 Journal of Dynamics and Control 9 263
[91] FitzHugh R 1961 Biophysical Journal 1 445
[92] Nagumo J, Arimoto S and Yoshizawa S 1962 Proceedings of the IRE 50 2061
[93] Zhan F and Liu S 2019 Nonlinear Dyn. 97 2675
[94] Longtin A 1993 Journal of Statal Physics 70 309
[95] Dmitrichev A S, Kasatkin D V, Klinshov V V, Kirillov S Y and Nekorkin V I 2018 Izvestiya VUZ Applied Nonlinear Dynamics 26 5
[96] ShiW, Min F and Yang S 2024 Chaos, Solitons & Fractals 188 115520
[97] Li B and He Z 2014 Nonlinear Dyn. 76 697
[98] Felicio C C and Rech P C 2015 Phys. Lett. A 379 2845
[99] Xia S and Lu Q S 2005 Chin. Phys. 14 1088
[100] Yan S, Wang J and Song J 2025 Integration 100 102280
[101] Tymoshchuk P V 2009 Neurocomputing 72 3191
[102] Tymoshchuk P V 2021 IOP Conference Series: Materials Science and Engineering 1016 012002
[103] He H, Yamanashi Y and Yoshikawa N 2022 IEEE Transactions on Applied Superconductivity 32 1300604
[104] Ma M, Lu Y and Li Yichuang Wang C 2023 Fractal and Fractional 7 82
[105] Cheng M, Wang K, Xu X and Mou J 2024 Cognitive Neurodynamics 18 3963
[106] Zou Y, Wang M, Zhang X and Iu H C 2025 arXiv:2505.24294
[107] Gao S, Zhang Z, Iu H C, Ding S and Cao Y 2025 IEEE Internet of Things Journal pp. 1-1
[108] Zhu W, Sun K, Wang H, Fu L and Minati L 2024 Chaos, Solitons & Fractals 186 115281
[109] Deng Q, Wang C, Yang G and Luo D 2025 IEEE Internet of Things Journal pp. 1-1
[110] Liu Y, Shen Y, Zhang H and Li Z 2024 Euro. Phys. J. Plus 139 235
[111] Chen L and Aihara K 1997 Physica D 104 286
[112] Cheng M, Wang K, Xu X and Mou J 2024 Cognitive Neurodynamics 18 3963
[113] Kandel E, Schwartz J, Jessell T, Siegelbaum S and Hudspeth A J 2013 Principles of Neural Science, Fifth Edition (Principles of Neural Science, Fifth Edition)
[114] Hopfield J J 1984 Proc. Natl. Acad. Sci. USA 81 3088
[115] Yu F, He T, He S, Tan B, Shi C and Lin H 2025 International Journal of Bifurcation and Chaos 35 2550146
[116] Bao B, Tang H, Su Y, Bao H, Chen M and Xu Q 2024 IEEE Transactions on Circuits and Systems I: Regular Papers 71 5907
[117] He S, Vignesh D, Rondoni L and Banerjee S 2023 Nonlinear Dyn. 111 21307
[118] Hioual A, Ouannas A, Oussaeif T E, Grassi G, Batiha IMand Momani S 2022 Fractal and Fractional 6 119
[119] Chua L and Yang L 1988 IEEE Transactions on Circuits and Systems 35 1257
[120] Grassi G 2001 IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 107
[121] Wang C, Luo D, Deng Q and Yang G 2024 Chaos, Solitons & Fractals 187 115471
[122] Lin H, Wang C, Deng Q, Xu C, Deng Z and Zhou C 2021 Nonlinear Dyn. 106 959
[123] Wang C, Guo S, Xu Y, Ma J, Tang J, Alzahrani F and Hobiny A 2017 Complexity 2017 5436737
[124] Lin H, Wang C, Sun Y and Yao W 2020 Nonlinear Dyn. 100 3667
[125] Wang Z, Bao H, Wu H, Chen M and Bao B 2023 Euro. Phys. J. Plus 138 545
[126] Li Y, Li C, Li Y, Moroz I and Yang Y 2024 Chaos, Solitons & Fractals 182 114800
[127] Ma T, Mou J and ChenW2025 Chaos, Solitons & Fractals 198 116537
[128] Han Z, Cao Y, Sun B and Mou J 2025 Euro. Phys. J. Spec. Top. 234 2731
[129] Qin M, Lai Q, Fortuna L and Zhao X W 2025 Nonlinear Dyn. 113 17095
[130] Yi C, Li C, Li Y and Yi Man Li R 2023 2023 IEEE International Conference on Memristive Computing and Applications (ICMCA) pp. 1-6
[131] Li K, Bao B, Ma J, Chen M and Bao H 2022 Chaos, Solitons & Fractals 165 112861
[132] Zhou X, Sun K, Wang H and Yao Z 2024 Nonlinear Dyn. 112 9547
[133] Ma J 2023 Journal of Zhejiang University-Science A 24 109
[134] Lin H, Wang C, Yu F, Sun J, Du S, Deng Z and Deng Q 2023 Mathematics 11 1369
[135] Lv M,Wang C, Ren G, Ma J and Song X 2016 Nonlinear Dyn. 85 1479
[136] Lv M and Ma J 2016 Neurocomputing 205 375
[137] Ma T, Mou J and ChenW2025 Chaos, Solitons & Fractals 190 115795
[138] Tang Z, Wang H, Zhu W and Sun K 2025 Chaos, Solitons & Fractals 192 116012
[139] Ma T, Mou J, Banerjee S and Cao Y 2023 Chaos, Solitons & Fractals 176 114113
[140] Liu B, Peng X and Li C 2024 AEU - International Journal of Electronics and Communications 178 155283
[141] Yu F, Xu S, Lin Y, He T, Xiao X, Cai S and Li Y 2024 Euro. Phys. J. Spec. Top. 234 2713
[142] Bao H, Fan J, Hua Z, Xu Q and Bao B 2025 IEEE Internet of Things Journal 12 31843
[143] Serrano F E and Pham V T 2025 Euro. Phys. J. Spec. Top. 234 2775
[144] Luo D, Wang C, Deng Q and Sun Y 2025 Nonlinear Dyn. 113 5811
[145] Zhiyuan F, Yan L, Guangyi W and Yana G 2024 Analog Integrated Circuits and Signal Processing 118 329
[146] Wang L, Gao H, Li C, et al. 2025 Euro. Phys. J. Spec. Top.
[147] Wang L, Zeng Z, Ge M F and Hu J 2018 Neural Networks 105 65
[148] Deng Q, Wang C, Yang G and Luo D 2025 IEEE Internet of Things Journal 12 25559
[149] Su X T 2017 Synchronization of coupled neural networks MA thesis (Zhejiang Normal University) (in Chinese)
[150] Zheng Y 2018 Biophysics 6 50
[151] Wu Z 2018 Study of Singular States in the FHN Model Ph.D. thesis (Beijing University of Posts and Telecommunications)
[152] Hizanidis J, Kanas V, Bezerianos A and Bountis T 2014 International Journal of Bifurcation & Chaos 24 1450030 |
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