Synergistic delay and strength tuning for logical operations in a chaotic neuron

doi:10.1088/1674-1056/ae5786

中国物理B ›› 2026, Vol. 35 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/ae5786

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Synergistic delay and strength tuning for logical operations in a chaotic neuron

Ying Xu(徐莹)†

School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China

收稿日期:2026-02-04 修回日期:2026-03-19 接受日期:2026-03-26 发布日期:2026-06-15
通讯作者: Ying Xu E-mail:uryysunshine@163.com
基金资助:
Project supported by the Key R&D Program of Shandong Province, China (Grant No. 2025CXPT087) and the National Natural Science Foundation of China (Grant No. 12402061).

Synergistic delay and strength tuning for logical operations in a chaotic neuron

Ying Xu(徐莹)†

School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China

Received:2026-02-04 Revised:2026-03-19 Accepted:2026-03-26 Published:2026-06-15
Contact: Ying Xu E-mail:uryysunshine@163.com
Supported by:
Project supported by the Key R&D Program of Shandong Province, China (Grant No. 2025CXPT087) and the National Natural Science Foundation of China (Grant No. 12402061).

摘要/Abstract

摘要： An improved FitzHugh-Nagumo neuron model is proposed, incorporating electromagnetic induction via a flux-controlled memristor and dual autaptic feedback with tunable strengths and delays. This brain-inspired unit can reliably perform AND and OR logic operations under chaotic driving, serving as a tunable nonlinear computing element. Systematic numerical analysis reveals that the synergistic interplay between autaptic delays and strengths plays a key role in achieving optimal logical stochastic resonance. Specifically, the system achieves near-perfect success rates within specific parameter regions, where a compensatory effect enables delay asymmetry to balance synaptic strength mismatch. Furthermore, at lower coupling strengths, a multiple logical resonance phenomenon is observed, in which the success probability exhibits multiple peaks as a function of synaptic delay. This work not only elucidates the dynamical mechanism underlying reliable neuronal logic operation but also provides a co-design principle for tuning neuromorphic circuits, with potential implications for low-power, high-flexibility computing hardware.

关键词: FitzHugh-Nagumo neuron model, memristor, multi-scale autapse, logical resonance, time delay

Abstract: An improved FitzHugh-Nagumo neuron model is proposed, incorporating electromagnetic induction via a flux-controlled memristor and dual autaptic feedback with tunable strengths and delays. This brain-inspired unit can reliably perform AND and OR logic operations under chaotic driving, serving as a tunable nonlinear computing element. Systematic numerical analysis reveals that the synergistic interplay between autaptic delays and strengths plays a key role in achieving optimal logical stochastic resonance. Specifically, the system achieves near-perfect success rates within specific parameter regions, where a compensatory effect enables delay asymmetry to balance synaptic strength mismatch. Furthermore, at lower coupling strengths, a multiple logical resonance phenomenon is observed, in which the success probability exhibits multiple peaks as a function of synaptic delay. This work not only elucidates the dynamical mechanism underlying reliable neuronal logic operation but also provides a co-design principle for tuning neuromorphic circuits, with potential implications for low-power, high-flexibility computing hardware.

Key words: FitzHugh-Nagumo neuron model, memristor, multi-scale autapse, logical resonance, time delay

中图分类号: (Ordinary differential equations)

02.30.Hq

02.30.Oz (Bifurcation theory) 05.45.-a (Nonlinear dynamics and chaos) 05.40.Ca (Noise)

Ying Xu(徐莹). Synergistic delay and strength tuning for logical operations in a chaotic neuron[J]. 中国物理B, 2026, 35(6): 60201-060201.

Ying Xu(徐莹). Synergistic delay and strength tuning for logical operations in a chaotic neuron[J]. Chin. Phys. B, 2026, 35(6): 60201-060201.

参考文献

[1] Roy K, Jaiswal A and Panda P 2019 Nature 575 607
[2] Wysoski S G, Benuskova L and Kasabov N 2010 Neural Networks 23 819
[3] Patino-Saucedo A, Rostro-Gonzalez H, Serrano-Gotarredona T and Linares-Barranco B 2020 Neural Networks 121 319
[4] Renart A, De La Rocha J, Bartho P, Hollender L, Parga N, Reyes A and Harris K D 2010 Science 327 587
[5] Wu Y, Deng L, Li G, Zhu J and Shi L 2018 Front. Neurosci. 12 331
[6] Lu S, Dai Z, Liu Y, Liu G, Yang H and Wang F 2019 Chin. J. Phys. 58 179
[7] Yang H, Yao Y and Ren J 2022 Chin. J. Phys. 77 124
[8] Yao Y and Yao C 2023 Nonlinear Dyn. 111 4807
[9] Huang H, Ren R and Deng K 2022 Chin. J. Phys. 77 269
[10] Brown D, Feng J and Feerick S 1999 Phys. Rev. Lett. 82 4731
[11] Xu Q, Chen X, Chen B, Wu H, Li Z and Bao H 2023 Nonlinear Dyn. 111 8737
[12] Murali K, Sinha S, Ditto W L and Bulsara A R 2009 Phys. Rev. Lett. 102 104101
[13] Wu F, Guo Y, Ma J and Jin W 2023 Appl. Math. Comput. 455 128131
[14] Zhou P, Xu Y and Ma J 2023 Physica A 620 128746
[15] Wang Z, Qiao Z, Zhou L and Zhang L 2017 Chin. J. Phys. 55 252
[16] Yu D, Yang L, Zhan X, Fu Z and Jia Y 2023 Nonlinear Dyn. 111 6757
[17] Wang X, Yu D, Li T and Jia Y 2023 Physica A 630 129247
[18] Wang X, Jia K and Ge M 2025 Chin. J. Phys. 97 1355
[19] Njitacke Z T, Takembo C N, Koumetio B N and Awrejcewicz J 2022 Nonlinear Dyn. 110 2793
[20] Ma J, Song X, Tang J and Wang C 2015 Neurocomputing 167 378
[21] Wang H, Ma J, Chen Y and Chen Y 2014 Commun. Nonlinear Sci. Numer. Simul. 19 3242
[22] Yao C, He Z, Nakano T, Qian Y and Shuai J 2019 Nonlinear Dyn. 97 1425
[23] Yilmaz E, Baysal V, Perc M and Ozer M 2016 Sci. China Technol. Sci. 59 364
[24] Baysal V, Erkan E and Yilmaz E 2021 Philos. Trans. R. Soc. A 379 20200237
[25] Zhao Z, Li L and Gu H 2020 Commun. Nonlinear Sci. Numer. Simul. 85 105250
[26] Markovic D, Mizrahi A, Querlioz D and Grollier J 2020 Nat. Rev. Phys. 2 499
[27] Xu K and Wang Z 2023 Neural Comput. Appl. 35 8785
[28] Zhou P, Xu Y and Ma J 2023 Physica A 620 128746
[29] Guo Y, Wang C and Ma J 2025 Phys. Lett. A 529 130069
[30] Sun G, Xu Y, Jin W and Ren G 2023 Physica A 625 129003
[31] Guo Y, Song X and Ma J 2025 Nonlinear Dyn. 113 1605
[32] Ma J and Guo Y 2024 Chaos Solitons Fractals 183 114925
[33] Xu Y and Qin H 2024 Chin. J. Phys. 92 1384
[34] Sun G and Xu Y 2025 Commun. Theor. Phys. 77 115001
[35] Ge M, Jia K, Wang X, Liu Y and Jiang Y 2025 Nonlinear Dyn. 113 26671
[36] Tuci E, Massera G and Nolfi S 2010 IEEE Trans. Evol. Comput. 14 885
[37] Ma J 2025 Nonlinear Dyn. 113 25365
[38] Li X and Xu Y 2024 Nonlinear Dyn. 112 2253
[39] Jia J, Xie Y, Wang C and Ma J 2024 Phys. Scr. 99 115030
[40] Xu Y and Li X 2025 AIMS Math. 10 10976
[41] Wang B, Lv M, Zhang X and Ma J 2024 Phys. Scr. 99 055225
[42] Mbeunga N K, Nana B andWoafo P 2021 Chaos Solitons Fractals 153 111484
[43] Ngongiah I K, Balamurali R, Kuiate G F, et al. 2023 Phys. Scr. 98 045221
[44] Pikovsky A S and Kurths J 1997 Phys. Rev. Lett. 78 775
[45] Tabor M and Weiss J 1981 Phys. Rev. A 24 2157
[46] Li Y, Schmid G, Haenggi P and Schimansky-Geier L 2010 Phys. Rev. E 82 061907
[47] Belykh I, De Lange E and Hasler M 2005 Phys. Rev. Lett. 94 188101
[48] Zhang H, Xu Y, Xu W and Li X 2012 Chaos 22 043130
[49] Storni R, Ando H, Aihara K, Murali K and Sinha S 2012 Phys. Lett. A 376 930

Synergistic delay and strength tuning for logical operations in a chaotic neuron

Synergistic delay and strength tuning for logical operations in a chaotic neuron

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