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Chin. Phys. B, 2023, Vol. 32(1): 010503    DOI: 10.1088/1674-1056/ac65f7
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Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

Zhi-Jun Li(李志军)1,†, Wen-Qiang Xie(谢文强)1, Jin-Fang Zeng(曾金芳)2, and Yi-Cheng Zeng(曾以成)2
1 School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China;
2 School of Physics and Optoelectronics, Xiangtan University, Xiangtan 411105, China
Abstract  Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.
Keywords:  fractional-order      multistable      neuron      firing      locally-active memristor  
Received:  04 March 2022      Revised:  28 March 2022      Accepted manuscript online:  11 April 2022
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  87.19.ll (Models of single neurons and networks)  
  87.19.lj (Neuronal network dynamics)  
Fund: Project supported by the National Key Research and Development Program of China (Grant No. 2018AAA0103300) and the National Natural Science Foundation of China (Grant Nos. 62171401 and 62071411).
Corresponding Authors:  Zhi-Jun Li     E-mail:

Cite this article: 

Zhi-Jun Li(李志军), Wen-Qiang Xie(谢文强), Jin-Fang Zeng(曾金芳), and Yi-Cheng Zeng(曾以成) Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse 2023 Chin. Phys. B 32 010503

[1] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[2] Hindmarsh J L and Rose R M 1984 Philos. Trans. R. Soc. Lond B Biol. Sci. 221 87
[3] FitzHugh R 1961 Biophys. J. 1 445
[4] Izhikevich E M 2004 IEEE Trans. Neural Networks 15 1063
[5] Morris C and Lecar H 1981 Biophys. J. 35 193
[6] Han F, Wang Z J and Fan H 2015 Chin. Phys. Lett. 32 040502
[7] Ding L X, Jia B and Li Y Y 2019 Acta Phys. Sin. 68 180502 (in Chinese)
[8] Lu Y M, Wang C H and Deng Q L 2022 Chin. Phys. B 31 060502
[9] Qi G and Wang Z 2020 Chin. Phys. B 30 120516
[10] Xu Y, Liu M and Zhu Z 2020 Chin. Phys. B 29 098704
[11] Yin L, Zheng R, Ke W, He Q and Zhang Y 2018 Nat. Comm. 9 4890
[12] Yilmaz E, Ozer M, Baysal V and Perc M 2016 Sci. Rep. 6 30914
[13] Zhao Z and Gu H 2017 Sci. Rep. 7 6760
[14] Strukov D B, Snider G S, Stewart D R, Williams and Stanley R 2008 Nature 453 80
[15] Chua L O 2015 Radioengineering 24 319
[16] Wang C, Xiong L, Sun J and Yao W 2019 Nonlinear Dyn. 95 2893
[17] Mannan Z I, Adhikari S P, Yang C, Budhathoki R K, Kim H and Chua L 2019 IEEE Trans. Neural Netw. Learn. Syst. 30 3458
[18] Wang C, Guo S and Xu Y 2017 Complexity 2017 5436737
[19] Wang H, Ma J and Chen Y 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 3242
[20] Ma J, Song X, Jin W and Wang C 2015 Chaos Solitons Fract. 80 31
[21] Qu L, Du L, Zhang H and Cao Z 2019 Int. J. Bifurcat. Chaos 29 1950202
[22] Yilmaz E, Baysal V, Perc M and Ozer M 2016 Sci. China Technol. Sc. 59 364
[23] Tripathi D, Pandey S K and Das S 2015 Appl. Math. Comput. 215 3645
[24] Hilfer R 2000 Applications of Fractional Calculus in Physics, 2nd edn. (Singapore: World Scientific) pp. 12-15
[25] Monje C A, Chen Y Q, Vinagre B M and Xue D 2010 Fractional-order Systems and Controls, 1st edn. (Springer Science & Business Media) pp. 89-162
[26] Lundstrom B N, Higgs M H, Spain W J and Fairhall A L 2018 Nat. Neurosci. 11 1335
[27] Magin R L 2014 Critical Review in Biomedical Engineering 32 10
[28] Yu Y, Shi M, Kang H, Chen M and Bao B 2020 Nonlinear Dyn. 100 891
[29] Alidousti J and Ghaziani 2017 Mathematical Models and Computer Simulations 9 390
[30] Meng F, Zeng X and Wang Z 2019 Nonlinear Dyn. 95 1615
[31] Meng F, Zeng X and Wang Z 2020 Int. J. Bifurcat. Chaos 30 2050044
[32] Malik S A and Mir A H 2020 IEEE ACM T. Comput. Bi. 11 1545
[33] Leng Y, Yu D, Hu Y, Yu S and Ye Z 2020 Chaos 30 033108
[34] Chua L O 2005 Int. J. Bifurcat. Chaos 15 3435
[35] Chua L O 2014 Semicond. Sci. Tech. 29 104001
[36] Gibson GA, Musunuru S, Zhang J, Vandenberghe K, Lee J and Cheng C 2016 Appl. Phys. Lett. 108 023505
[37] Li Z, Guo Z, Wang M and Ma M 2021 AEU-Int. J. Electron. Commun. 142 153995
[38] Jin P, Wang G, Lu H and Fernando T A 2017 IEEE T. Circuits Sys. II 65 246
[39] Xu B, Wang G, Lu H, Yu S and Yuan F 2019 Nonlinear Dyn. 96 765
[40] Yuan F, Wang G and Wang X 2016 Chaos 26 073107
[41] Zhu M, Wang C, Deng Q and Hong Q 2020 Int. J. Bifurcat. Chaos 30 2050184
[42] Li Z, Zhou H, Wang M and Ma M 2021 Nonlinear Dyn. 104 1455
[43] Lin H, Wang C, Sun Y and Wei Y 2020 Nonlinear Dyn. 100 3667
[44] Li Z and Zhou H 2021 Electron. Lett. 57 715
[45] Xie W, Wang C and Lin H 2021 Nonlinear Dyn. 104 4523
[46] Yang N, Xu C, Wu C, Jia R and Liu C 2019 Nonlinear Dyn. 97 33
[47] Chang H, Wang Z, Li Y and Chen G 2018 Int. J. Bifurcat. Chaos 28 1850105
[48] Matignon D 2016 Computational Engineering in Systems Applications 2 963
[49] Adomian G 1998 J. Math. Anal. Appl. 135 501
[50] Tavazoei M S and Haeri M 2009 Automatica 45 1886
[51] Kaslik E and Sivasundaram S 2012 Nonlinear Anal. 13 1489
[52] Danca M F, Fečkan M, Kuznetsov N V and Chen G 2018 Nonlinear Dyn. 91 2523
[53] Danca M F, Fečkan M and Chen G 2017 Nonlinear Dyn. 89 1889
[54] Kang Y M, Xie Y, Lu J C and Jiang J 2015 Nonlinear Dyn. 82 1259
[55] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[56] Danca M F and Kuznetsov N 2018 Int. J. Bifurcat. Chaos 28 1850067
[57] Bandy D K, Burton E K, Hall J R, Chapman D M and Elrod J T 2021 Chaos 31 013120
[58] Hall J R, Burton E K, Chapman D M and Bandy D K 2021 Applied Sciences 11 9905
[59] Chen X, Liu C and Wang F 2008 Chin. Phys. B 17 1664
[60] Shao S, Min F and Ma M 2013 J. Phys. 62 130504 (in Chinese)
[61] Zhou C, Li Z and Xie F 2019 Eur. Phys. J. Plus 134 73
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