Interaction function of coupled bursting neurons

doi:10.1088/1674-1056/25/6/060502

中国物理B ›› 2016, Vol. 25 ›› Issue (6): 60502-060502.doi: 10.1088/1674-1056/25/6/060502

Interaction function of coupled bursting neurons

Xia Shi(石霞), Jiadong Zhang(张佳栋)

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

收稿日期:2015-12-21 修回日期:2016-02-16 出版日期:2016-06-05 发布日期:2016-06-05
通讯作者: Xia Shi E-mail:shixiabupt@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272065 and 11472061).

Interaction function of coupled bursting neurons

Xia Shi(石霞), Jiadong Zhang(张佳栋)

School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received:2015-12-21 Revised:2016-02-16 Online:2016-06-05 Published:2016-06-05
Contact: Xia Shi E-mail:shixiabupt@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272065 and 11472061).

摘要/Abstract

摘要：

The interaction functions of electrically coupled Hindmarsh-Rose (HR) neurons for different firing patterns are investigated in this paper. By applying the phase reduction technique, the phase response curve (PRC) of the spiking neuron and burst phase response curve (BPRC) of the bursting neuron are derived. Then the interaction function of two coupled neurons can be calculated numerically according to the PRC (or BPRC) and the voltage time course of the neurons. Results show that the BPRC is more and more complicated with the increase of the spike number within a burst, and the curve of the interaction function oscillates more and more frequently with it. However, two certain things are unchanged: φ=0, which corresponds to the in-phase synchronization state, is always the stable equilibrium, while the anti-phase synchronization state with φ=0.5 is an unstable equilibrium.

关键词: phase response curve, burst phase response curve, interaction function, phase locking

Abstract:

Key words: phase response curve, burst phase response curve, interaction function, phase locking

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Xt (Synchronization; coupled oscillators)

石霞, 张佳栋. Interaction function of coupled bursting neurons[J]. 中国物理B, 2016, 25(6): 60502-060502.

Xia Shi(石霞), Jiadong Zhang(张佳栋). Interaction function of coupled bursting neurons[J]. Chin. Phys. B, 2016, 25(6): 60502-060502.

参考文献 35

[1]	Kuramoto Y and Nishikawa I 1987 J. Stat. Phys. 49 569
[2]	Acebrón J A, Bonilla L L, Vicente C J P, Ritort F and Spigler R 2005 Rev. Mod. Phys. 77 137
[3]	Wiener N 1958 Nonlinear Problems in Random Theory (Cambridge: MIT Press)
[4]	Wiener N 1961 Cybernetics (Cambridge: MIT Press)
[5]	Winfree A T 1967 J. Theor. Biol. 16 15
[6]	Strogatz S H 2000 Physica D 43 1
[7]	Ermentrout B 1998 Rep. Prog. Phys. 61 353
[8]	Perez V J L, Galán R F, Dominguez L, Leshchenko Y, Lo S, Belkas J and Erra R G 2007 Phys. Rev.E 76 061912
[9]	Rusin C G, Johnson S E, Kapur J and Hudson J L 2011 Phys.Rev. E 84 066202
[10]	Zhu Y, Hsieh Y H, Dhingra R R, Dick T E, Jacono F J and Galán R F 2013 Phys. Rev. E 87 022709
[11]	Hansel D, Mato G, and Meunier C 1995 Neural Comput. 7 307
[12]	Neu J 1979 SIAM J. Appl. Math. 37 307
[13]	Ermentrout G B and Kopell B 1991 J. Math. Biol. 29 195
[14]	Hoppensteadt F C and Izhikevich E M 1997 Weakly Connected Neural Networks (New York: Springer)
[15]	VanVreeswijk C, Abbott L F and Ermentrout G B 1994 J. Comput. Neurosci. 1 313
[16]	Smeal R M, Ermentrout G B and White J A 2010 Philos. Trans. R. Soc. Lond. B 365 2407
[17]	Wang X J 2010 Physiol. Rev. 90 1195
[18]	Dodla R and Wilson C J 2013 Phys. Rev. E 88 042704
[19]	Wiercigroch M, Ji Q B, Han F and Lu Q S 2009 Chin. Phys. B 18 482
[20]	Lu Q S, Shi X and Wang H X 2010 Chin. Phys. B 19 060509
[21]	Hossein G N, Asad A and Morteza K 2013 Chin. Phys. B 22 070502
[22]	Schultheiss N W, Prinz A A and Butera R J 2014 Phase Response Curves in Neuroscience (Berlin: Springer)
[23]	Ermentrout G B 2002 Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students (Philadelphia: Society for Industrial and Applied Mathematics)
[24]	Novienko V, and Pyragas K 2012 Nonlinear Dynamics 67 517
[25]	Guevara M R, Glass L, Mackey M C and Shier A 1983 IEEE Trans. Syst. Man Cybern. SMC-13 790
[26]	Govaerts W and Sautois B 2006 Neural Comput. 18 817
[27]	Ermentrout G B 1996 Neural Comput. 8 979
[28]	Sherwood W E and Guckenheimer J 2010 Siam J. Appl. Dyn. Sys. 9 659
[29]	Hindmarsh J L and Rose R M 1984 Proc. Roy. Soc. Lond. B 221 87
[30]	Wang W, Perez G and Cerdeira H A 1993 Phys. Rev. E 47 2893
[31]	Wang W, Chen G and Wang Z D 1997 Phys. Rev. E 56 3728
[32]	Shi X and Lu Q S 2005 Chin. Phys. 14 0077
[33]	Izhikevich E M 2006 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (SpringerLink)
[34]	Kuramoto Y 1984 Chemical Oscillations, Waves, and Turbulence (Berlin: Springer-Verlag)
[35]	Ermentrout G B and Kleinfeld D 2001 Neuron 29 33

Interaction function of coupled bursting neurons

Interaction function of coupled bursting neurons

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