Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

doi:10.1088/1674-1056/ac16cc

Abstract The firing of a neuron model is mainly affected by the following factors:the magnetic field, external forcing current, time delay, etc. In this paper, a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed. A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons. Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns, such as spiking firings, bursting firings, and chaotic firings, and enable neurons to generate larger firing amplitudes. The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing. Based on the existing medical treatment background of mental illness, the effects of time lag in the coupling process against neuron firing are studied. The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay, and keep periodic firing under a wide range of external forcing current.

Keywords: bi-Hindmarsh and Rose (HR) neuron model memristor magnetic coupling time delay

Received: 29 April 2021
Revised: 18 July 2021
Accepted manuscript online: 22 July 2021

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	87.15.-v	(Biomolecules: structure and physical properties)
	87.15.A-	(Theory, modeling, and computer simulation)
	84.35.+i	(Neural networks)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 61873186).

Corresponding Authors: Guoyuan Qi
E-mail: guoyuanqisa@qq.com

Cite this article:

Guoyuan Qi(齐国元) and Zimou Wang(王子谋) Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay 2021 Chin. Phys. B 30 120516

[1] Bertram R, Butte M J, Kiemel T and Sherman A 1995 B. Math. Biol. 57 413
[2] Ma J and Tang J 2017 Nonlinear Dyn. 89 1569
[3] Xu Y, Ma J, Zhan X, Yang L and Jia Y 2019 Cogn. Neurodyn. 13 601
[4] Bao B, Yang Q and Zhu D 2020 Nonlinear Dyn. 99 2339
[5] Corinto F, Ascoli A and Lanza V 2011 The 2011 International Joint Conference on Neural Networks 2402
[6] Ren G, Xu Y and Wang C 2017 Nonlinear Dyn. 88 893
[7] Yu H J and Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese)
[8] Yu Y, Hao Y and Wang Q 2020 Neural networks 122 308
[9] Jeyasothy A, Sundaram S and Sundararajan N 2018 IEEE Trans. Neural. Netw. Learn Syst. 30 1231
[10] Xu Y, Liu M H. Zhu Z G and Ma J 2020 Chin. Phys. B 29 098704
[11] Hodgkin A L and Huxley A F 1952 The Journal of Physiology 117 500
[12] Fitzhugh R 1961 Biophys. J. 1 445
[13] Hindmarsh J L and Rose R M 1982 Nature 296 162
[14] Hindmarsh J L and Rose R M 1982 Nature 299 375
[15] Hindmarsh J L and Rose R M 1984 Proceedings of the Royal Society B:Biological Sciences 221 87
[16] Chua L 1971 IEEE Trans. Circuits Syst. 18 507
[17] Bao B, Qian H, Xu Q, Chen M, Wang J and Yu Y 2017 Frontiers Comput. Neurosci. 11 81
[18] Lin H and Wang C 2020 Appl. Math. Comput. 369 124840
[19] Wu F, Ma J and Zhang G 2019 Appl. Math. Comput. 347 590
[20] Ma J, Wu F Q and Wang C N 2017 Mod. Phys. B 31 1650251
[21] Wu J, Xu Y and Ma J 2017 Plos One 12 1
[22] Lv M and Ma J 2016 Neurocomputing 205 375
[23] Bao H, Hu A, Liu W and Bao B C 2019 IEEE Trans. Neural. Netw. Learn Syst. 117 500
[24] Lin H and Wang C H 2020 Nonlinear Dyn. 99 2369
[25] Lin H, Wang C H, Sun Y C and Wei Yao 2020 Nonlinear Dyn. 100 3667
[26] Ren G D, Wu G and Ma J 2015 Acta Phys. Sin. 64 058702 (in Chinese)
[27] Lv M, Wang C and Ren G 2016 Nonlinear Dyn. 85 1479
[28] Eshraghian K, Kavehei O and Cho K R 2012 Proc. IEEE 100 1991
[29] Ostojic S, Brunel N and Hakim V 2009 J. Neurosci. 29 10234
[30] 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
[31] Tan Y M and Wang C H 2020 Chaos 30 053118
[32] Ma J, Lv M and Zhou P 2017 P. Math. Comput. 307 321
[33] Ma J, Wu F Q and Wang C N 2016 Mod. Phys. B. 31 1650251
[34] Parastesh F, Rajagopal K and Karthikeyan A 2018 Cogn. Neurodynamics. 12 607
[35] Usha K and Subha P A 2019 Chin. Phys. B 28 020502
[36] Xu Y, Jia Y, Ma J, Alsaedi A and Ahmad B 2017 Chaos, Solitons, and Fractals 104 435
[37] Xu F, Zhang J, Fang T, Huang S and Wang M 2018 Nonlinear Dyn. 92 1395
[38] Bao H, Liu W and Hu A 2019 Nonlinear Dyn. 95 43
[39] Qin H X, Ma J and Jin W 2014 Sci. Chin. Technol. Sci. 57 936
[40] Han F, Wang Z J, Fan H and Gong T 2015 Chin. Phys. Lett. 32 040502
[41] Lakshmanan S, Lim C P, Nahavandi S, Prakash M and Balasubramaniam P 2016 IEEE Trans. Neural. Netw. Learn Syst. 28 1953
[42] Steur E, Murguia C and Fey R H B 2016 Int. J. Bifurcat. Chaos 26 1
[43] Huang S F, Zhang J Q, Wang M S and Hu C K 2018 Physica A 499 88
[44] Fan D and Wang Q 2018 Phys. Rev. E 98 052414
[45] Fan D, Zhang L and Wang Q 2018 Nonlinear Dyn. 94 2807
[46] Izhikevich E M 2000 Bifurc. Chaos 10 1171
[47] Yang M, Liu Z, Li L, Xu Y, Liu H, Gu H and Ren W 2009 Bifurc. Chaos 19 453
[48] Skokos Ch 2010 Lect. Notes Phys. 790 63
[49] Schrader L M, Stem J M and Koski L 2004 Clin. Neurophysiol. 115 2728
[50] Ardolino G, Bossi B, Barbieri S and Priori A 2005 J. Physiol. 568 653
[51] Theodore W H 2003 Epilepsy Curr. 3 191

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Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

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