Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

doi:10.1088/1674-1056/21/1/010203

Abstract The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.

Keywords: neuronal nursting minimal model synchronization

Received: 13 July 2011
Revised: 15 August 2011
Accepted manuscript online:

PACS:	02.30.Ks	(Delay and functional equations)
	05.45.Xt	(Synchronization; coupled oscillators)

Fund: Project supported by the Serbian Ministry of Science (Grant Nos. 171017 and 174010).

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Nebojša Vasović, Nikola Burić, Kristina Todorović, and Ines Grozdanović Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses 2012 Chin. Phys. B 21 010203

[1]	Strogatz S H 2003 Synchronization: The Emerging Science of Spontaneous Order (New York: Hyperion)
[2]	Pikovsky A, Rosenblum M and Kurths J 2001 Synchronization. A Universal Concept in Nonlinear Sciences (Cambridge: Cambridge University Press)
[3]	Kandel E R, Schwartz J H and Jessel T M 1991 Principles of Neural Science 3rd edn (New York: Elsevier)
[4]	Kelso J A S 1995 Dynamic Patterns: The Self-Organization of Brain and Behavior (Cambridge MA: MIT Press)
[5]	Izhikevich E M 2005 Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Cambridge MA: MIT Press)
[6]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[7]	Kopell N and Ermentrout B 2004 Proc. Natl. Acad. Sci. USA 101 15482
[8]	Belykh I, de Lange E and Hasler M 2005 Phys. Rev. Lett. 94 188101
[9]	Gan C B, Perc M and Wang Q Y 2010 Chin. Phys. B 19 040508
[10]	Wang Q, Perc M, Duan Z and Chen G 2009 Phys. Rev. E 80 026206
[11]	Wang Q, Perc M, Duan Z and Chen G 2009 Chaos 19 023112
[12]	Wang Q, Duan Z, Perc M and Chen G 2008 Euro. Phys. Lett. 83 50008
[13]	Wang Q, Perc M, Duan Z and Chen G 2010 Physica A 389 3299
[14]	Wang Q, Chen G and Perc M 2011 PLoS ONE 6 e15851
[15]	FitzhHugh R 1955 Bull. Math. Biophys. 17 257
[16]	Nagumo J, Arimoto S and Yoshizava S 1962 Proc. IREE 50 2061
[17]	Buri? N and Todorovi? D 2003 Phys. Rev. E 67 066222
[18]	Buri? N, Grozdanovi? I and Vasovi? N 2005 Chaos Soliton. Fract. 23 1221
[19]	Hindmarch J L and Rose R M A 1984 Proc. R Soc. London Ser. B 221 87
[20]	Yu H and Peng J 2006 Chaos Soliton. Fract. 29 343
[21]	Abarbanel H D I et al. 1996 Neural Computation 8 1567
[22]	Dhamala M, Jirsa V K and Ding M 2004 Phys. Rev. Lett. 92 074104
[23]	Buric N and Rankovic D 2007 Phys. Lett. A 363 282
[24]	Buric N, Todorovic K and Vasovic N 2008 Phys. Rev. E 78 036211
[25]	Izhikevich E M 2001 Sirev 43 315
[26]	Somers D and Kopell N 1993 Cibernet 68 393
[27]	Strogatz S H 1998 Nature 394 316

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Synchronization of the minimal models of bursting neurons coupled by delayed chemical or electrical synapses

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