Rhythm dynamics of complex neuronal networks with mixed bursting neurons

doi:10.1088/1674-1056/22/4/040505

Abstract Spatiotemporal order and rhythm dynamics of a complex neuronal network with mixed bursting neurons are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neuronal network. A parameter r is introduced to denote the ratio of the short bursting neurons in the network. Then we investigate the effect of the ratio on the rhythm dynamics of the neuronal network. The critical value of r is derived, and the neurons in the network are always keeping short bursting when the ratio r is larger than the critical value.

Keywords: rhythm dynamics complex network neuron

Received: 04 August 2012
Revised: 28 September 2012
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	87.19.lj	(Neuronal network dynamics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272065 and 11102041) and the Fundamental Research Funds for the Central Universities (Grant No. 2011RC0702).

Corresponding Authors: Shi Xia
E-mail: berthashi@yahoo.com.cn

Cite this article:

Lü Yong-Bing (吕永兵), Shi Xia (石霞), Zheng Yan-Hong (郑艳红) Rhythm dynamics of complex neuronal networks with mixed bursting neurons 2013 Chin. Phys. B 22 040505

[1]	Buzsaki G 2006 Rhythms of the Brain (New York: Oxford University Press)
[2]	Fries P, Reynolds J H, Rorie A E and Desimone R 2001 Science 29 1560
[3]	Salinas E and Sejnowski T J 2001 Nature Neuroscience 2 539
[4]	Milton J and Jung P 2003 Epilepsy as a Dynamic Disease Chap. 7 (Berlin: Springer-Verlag)
[5]	Belykh I, de Lange E and Hasler M 2005 Phys. Rev. Lett. 94 188101
[6]	Rulkov N F 2001 Phys. Rev. Lett. 86 183
[7]	Yan C K and Wang R B 2012 Chin. Phys. Lett. 29 090501
[8]	Chai Y, Lü L and Chen L Q 2012 Chin. Phys. B 21 030506
[9]	Zhang Q L and Lü L 2011 Chin. Phys. B 20 010510
[10]	Batista C A S, Batista A M, Pontes J A C, Viana R L and Lopes S R 2007 Phys. Rev. E 76 016218
[11]	Batista C A S, Batista A M, Pontes J A C, Viana R L and Lopes S R 2009 Chaos, Solitons and Fractals 41 2220
[12]	Ivanchenko M V, Osipov G V, Shalfeev V D and Kurths J 2004 Phys. Rev. Lett. 93 134101
[13]	Ivanchenko M V, Osipov G V, Shalfeev V D and Kurths J 2007 Phys. Rev. Lett. 98 108101
[14]	Yu H T, Wang J, Deng B, Wei X L, Wong Y K, Chan W L, Tsang K M and Yu Z Q 2011 Chaos 21 013127
[15]	Shi X and Lu Q S 2009 Physica A 388 2410
[16]	Shi X, Lu Q S and Wang H X 2012 Int. J. Bifur. Chaos 22 1250101
[17]	Izhikevich E M 2005 Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting (Cambridge: MIT Press)
[18]	Lisman J E 1997 Trends Neurosci. 20 38
[19]	Nebojša V, Nikola B, Kristina T and Ines G 2012 Chin. Phys. B 21 010203
[20]	Wang Q Y, Chen G R and Perc M 2011 Plos One 6 e15851
[21]	Wu H, Hou Z and Xin H 2010 Chaos 20 043140
[22]	Du Q W and Xiao S L 2007 Europhys. Lett. 78 68004
[23]	Wang Q Y, Sanjuăn M A F and Chen G R 2012 Neurocomputing 81 60
[24]	Van den Heuvel M P, Stam C J, Boersma M and Hulshoff Pol H E 2008 Neuroimage. 43 528
[25]	Watts D J and Strogatz S H 1998 Nature 393 440

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