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Chin. Phys. B, 2014, Vol. 23(5): 050510    DOI: 10.1088/1674-1056/23/5/050510
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Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation

Jia Bing (贾冰)
Center for Computational System Biology, School of Mathematical Science, Fudan University, Shanghai 200433, China
Abstract  The coexistence of a resting condition and period-1 firing near a subcritical Hopf bifurcation point, lying between the monostable resting condition and period-1 firing, is often observed in neurons of the central nervous systems. Near such a bifurcation point in the Morris-Lecar (ML) model, the attraction domain of the resting condition decreases while that of the coexisting period-1 firing increases as the bifurcation parameter value increases. With the increase of the coupling strength, and parameter and initial value dependent synchronization transition processes from non-synchronization to compete synchronization are simulated in two coupled ML neurons with coexisting behaviors: one neuron chosen as the resting condition and the other the coexisting period-1 firing. The complete synchronization is either a resting condition or period-1 firing dependent on the initial values of period-1 firing when the bifurcation parameter value is small or middle and is period-1 firing when the parameter value is large. As the bifurcation parameter value increases, the probability of the initial values of a period-1 firing neuron that lead to complete synchronization of period-1 firing increases, while that leading to complete synchronization of the resting condition decreases. It shows that the attraction domain of a coexisting behavior is larger, the probability of initial values leading to complete synchronization of this behavior is higher. The bifurcations of the coupled system are investigated and discussed. The results reveal the complex dynamics of synchronization behaviors of the coupled system composed of neurons with the coexisting resting condition and period-1 firing, and are helpful to further identify the dynamics of the spatiotemporal behaviors of the central nervous system.
Keywords:  synchronization      neuronal network      Hopf bifurcation      coexistence  
Received:  06 September 2013      Revised:  29 October 2013      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  87.18.Tt (Noise in biological systems)  
  87.18.Hf (Spatiotemporal pattern formation in cellular populations)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11072135).
Corresponding Authors:  Jia Bing     E-mail:  jiabing427@163.com,jiabing427@gmail.com
About author:  05.45.Xt; 87.18.Tt; 87.18.Hf

Cite this article: 

Jia Bing (贾冰) Synchronization transition of a coupled system composed of neurons with coexisting behaviors near a Hopf bifurcation 2014 Chin. Phys. B 23 050510

[1] Arenas A, Díaz-Guilera A, Kurths J, Moreno Y and Zhou C S 2008 Phys. Rep. 469 93
[2] Boccaletti S, Kurths J, Osipov G, Valladares D L and Zhou C S 2002 Phys. Rep. 366 1
[3] Wang C N, Ma J, Tang J and Li Y L 2010 Commun. Theor. Phys. 53 382
[4] Ma J, Huang L, Wang C N and Pu Z S 2013 Commun. Theor. Phys. 59 233
[5] Wu X and Ma J 2013 PLoS ONE 8 e55403
[6] Sun X J, Lei J Z, Perc M, Kurths J and Chen G R 2011 Chaos 21 016110
[7] Zhang N, Zhang H M, Liu Z Q, Ding X L, Yang M H, Gu H G and Ren W 2009 Chin. Phys. Lett. 26 110501
[8] Yuan L, Liu Z Q, Zhang H M, Yang M H, Wei C L, Ding X L, Gu H G and Ren W 2011 Chin. Phys. B 20 020508
[9] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G and Ren W 2009 Chin. Phys. Lett. 26 030504
[10] Tang Z, Li Y Y, Xi L, Jia B and Gu H G 2012 Commun. Theor. Phys. 57 61
[11] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G and Ren W 2010 Physica A 389 2642
[12] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G and Ren W 2009 Chin. Phys. Lett. 26 030504
[13] Singer W and Gray C M 1995 Annu. Rev. Neurosci. 18 555
[14] Llinas R and Ribary U 1993 Proc. Natl. Acad. Sci. USA 90 2078
[15] Hartline D K and Gassie D V 1979 Biol. Cybern. 33 209
[16] Buzsaki G and Draguhn A 2004 Science 304 1926
[17] Choi J W, Jung K Y, Kim C H and Kim K H 2010 Neurosci. Lett. 468 156
[18] Gray C M, König P, Engel A K and Singer W 1989 Nature 338 334
[19] Fujisaka H and Yamada T 1983 Prog. Theor. Phys. 69 32
[20] Kim K H, Yoon J, Kim J H and Jung K Y 2008 Brain Res. 1236 105
[21] Pisarchik A N, Jaimes-Reátegui R, Villalobos-Salazar J R, Garcia-Lopez J H and Boccaletti S 2006 Phys. Rev. Lett. 96 244102
[22] Pisarchik A N, Jaimes-Reátegui R and García-López J 2008 Phil. Trans. R. Soc. A 366 459
[23] Ruiz-Oliveras F R and Pisarchik A N 2009 Phys. Rev. E 79 016202
[24] Izhikevich E M 2000 Int. J. Bifurc. Chaos 10 1171
[25] Zhang Y, Tan K K and Lee T H 2003 Neural Comput. 15 639
[26] Zhang Y and Tan K K 2004 IEEE Trans. Neural Netw. 15 329
[27] Tateno T and Pakdaman K 2004 Chaos 14 511
[28] Wang Q Y, Duan Z S, Feng Z S, Chen G R and Lu Q S 2008 Physica A 387 4404
[29] Fröhlich F and Bazhenov M 2006 Phys. Rev. E 74 031922
[30] Cymbalyuk G and Shilnikov A 2005 J. Comput. Neurosci. 18 255
[31] Gu H G, Yang M H, Li L, Liu Z Q and Ren W 2003 Phys. Lett. A 319 89
[32] Yang M H, Liu Z Q, Li L, Xu Y L, Liu H J, Gu H G and Ren W 2009 Int. J. Bifurc. Chaos 19 453
[33] Gu H G, Ren W, Lu Q S, Wu S G and Chen W J 2001 Phys. Lett. A 285 63
[34] Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q and Ren W 2011 Int. J. Mod. Phys. B 25 3977
[35] Guttman R, Lewis S and Rinzel J 1980 J. Physiol. 305 377
[36] Lechner H A, Baxter D A, Clark J W and Byrne J H 1996 J. Neurophysiol. 75 957
[37] Tateno T, Harsch A and Robinson H P C 2004 J. Neurophysiol. 92 2283
[38] Prescott S A, Ratté S, Koninck Y D and Sejnowski T J 2008 J. Neurophysiol. 100 3030
[39] Ruiz-Oliveras F R and Pisarchik A N 2009 Phys. Rev. E 79 016202
[40] Gu H G, Li Y Y, Jia B and Chen G R 2013 Physica A 392 3281
[41] Lindner B, García-Ojalvo J, Neiman A and Schimansky-Geier L 2004 Phys. Rep. 392 321
[42] Wang H X, Wang Q Y, Lu Q S and Zheng Y H 2013 Cogn. Neurodyn. 7 121
[43] Ding X L, Li Y Y, Li Q H, Gu H G and Ren W 2009 J. Dyn. Control. 7 297
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