|
|
Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns |
Gu Hua-Guang (古华光)a, Chen Sheng-Gen (陈胜根)a, Li Yu-Ye (李玉叶)b |
a School of Aerospace Engineering and Applied Mechanic, Tongji University, Shanghai 200092, China; b Mathematics & Statistics Institute, Chifeng University, Chifeng 024000, China |
|
|
Abstract We investigated the synchronization dynamics of a coupled neuronal system composed of two identical Chay model neurons. The Chay model showed coexisting period-1 and period-2 bursting patterns as a parameter and initial values are varied. We simulated multiple periodic and chaotic bursting patterns with non-(NS), burst phase (BS), spike phase (SS), complete (CS), and lag synchronization states. When the coexisting behavior is near period-2 bursting, the transitions of synchronization states of the coupled system follows very complex transitions that begins with transitions between BS and SS, moves to transitions between CS and SS, and to CS. Most initial values lead to the CS state of period-2 bursting while only a few lead to the CS state of period-1 bursting. When the coexisting behavior is near period-1 bursting, the transitions begin with NS, move to transitions between SS and BS, to transitions between SS and CS, and then to CS. Most initial values lead to the CS state of period-1 bursting but a few lead to the CS state of period-2 bursting. The BS was identified as chaos synchronization. The patterns for NS and transitions between BS and SS are insensitive to initial values. The patterns for transitions between CS and SS and the CS state are sensitive to them. The number of spikes per burst of non-CS bursting increases with increasing coupling strength. These results not only reveal the initial value- and parameter-dependent synchronization transitions of coupled systems with coexisting behaviors, but also facilitate interpretation of various bursting patterns and synchronization transitions generated in the nervous system with weak coupling strength.
|
Received: 02 September 2014
Revised: 15 October 2014
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 Nos. 11372224 and 11402039) and the Fundamental Research Funds for Central Universities designated to Tongji University (Grant No. 1330219127). |
Corresponding Authors:
Gu Hua-Guang
E-mail: guhuaguang@tongji.edu.cn
|
About author: 05.45.Xt; 87.18.Tt; 87.18.Hf |
Cite this article:
Gu Hua-Guang (古华光), Chen Sheng-Gen (陈胜根), Li Yu-Ye (李玉叶) Complex transitions between spike, burst or chaos synchronization states in coupled neurons with coexisting bursting patterns 2015 Chin. Phys. B 24 050505
|
[1] |
Arenas A, Díaz-Guilera A, Kurths J, Moreno Y and Zhou C S 2008 Phys. Rep. 469 93
|
[2] |
Glass L 2001 Nature 410 27
|
[3] |
Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821
|
[4] |
Singer W and Gray C M 1995 Annu. Rev. Neurosci. 18 555
|
[5] |
Llinás R and Ribary U 1993 Proc. Natl. Acad. Sci. USA 90 2078
|
[6] |
Hartline D K 1979 Biol. Cybern. 33 223
|
[7] |
Kim K H, Yoon J, Kim J H and Junq K Y 2008 Brain Res. 1236 105
|
[8] |
Choi J W, Jung K Y, Kim C H and Kim K H 2010 Neurosci. Lett. 468 156
|
[9] |
Bartsch R, Kantelhardt J W, Penzel T and Havlin S 2007 Phys. Rev. Lett. 98 54102
|
[10] |
Buzsáki G and Draguhn A 2004 Science 304 1926
|
[11] |
Gray C M, König P, Engel A K and Singer W 1989 Nature 338 334
|
[12] |
Jefferys J G and Haas H L 1982 Nature 300 448
|
[13] |
Kepecs A, Wang X J and Lisman J 2002 J. Neurosci. 22 9053
|
[14] |
Kepecs A and Lisman J 2003 Network 14 103
|
[15] |
Sun X J, Lei J Z, Perc M, Kurths J and Chen G R 2011 Chaos 21 016110
|
[16] |
Ando H, Suetani H, Kurths J and Aihara K 2012 Phys. Rev. E 86 016205
|
[17] |
Batista C A, Viana R L, Ferrari F A, Lopes S R, Batista A M and Coninck J C 2013 Phys. Rev. E 87 042713
|
[18] |
Gu H G, Pan B B and Xu J 2014 EPL 106 50003
|
[19] |
Gu H G, Li Y Y, Jia B and Chen G R 2013 Physica A 392 3281
|
[20] |
Droz M and Lipowski A 2003 Phys. Rev. E 67 056204
|
[21] |
Liang X, Tang M, Dhamala M and Liu Z 2009 Phys. Rev. E 80 066202
|
[22] |
Wang Q Y, Chen G R and Perc M 2011 PLoS One 6 e15851
|
[23] |
Ozbudak E M, Thattai M, Lim H N, Shraiman B I and Van Oudenaarden A 2004 Nature 427 737
|
[24] |
Guttman R, Lewis S and Rinzel J 1980 J. Physiol. 30 377
|
[25] |
Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
|
[26] |
Tateno T and Pakdaman K 2004 Chaos 14 511
|
[27] |
Lechner H A, Baxter D A, Clark J W and Byrne J H 1996 J. Neurophysiol. 75 957
|
[28] |
Fröhlich F and Bazhenov M 2006 Phys. Rev. E 74 031922
|
[29] |
Cymbalyuk G and Shilnikov A 2005 J. Comput. Neurosci. 18 255
|
[30] |
Xu Y L, Yang M H, Liu Z Q, Liu H J, Gu H G and Ren W 2007 Dyn. Contin. Discrete Impuls. Syst. Ser. B 14 35
|
[31] |
Pisarchik A N, Jaimes-Reátegui R and García-López J H 2008 Phil. Trans. R. Soc. A 366 459
|
[32] |
Pisarchik A N, Jaimes-Rem átegui R and García-López J H 2008 Int. J. Bifurcat. Chaos 18 1801
|
[33] |
Pisarchik A N, Jaimes-Reátegui R, Villalobos-Salazar J R, García-López J H and Boccaletti S 2006 Phys. Rev. Lett. 96 244102
|
[34] |
Sausedo-Solorio J M and Pisarchik A N 2011 Phys. Lett. A 375 3677
|
[35] |
Ruiz-Oliveras F R and Pisarchik A N 2009 Phys. Rev. E 79 016202
|
[36] |
Wang Q Y, Duan Z S, Feng Z S, Chen G R and Lu Q S 2008 Physica A 387 4404
|
[37] |
Gu H G, Li Y Y, Jia B and Chen G R 2013 Physica A 392 3281
|
[38] |
Bing J 2014 Chin. Phys. B 23 050510
|
[39] |
Chay T R 1985 Physica D 16 233
|
[40] |
Gu H G 2013 Chaos 23 023126
|
[41] |
Gu H G and Xiao W W 2014 Int. J. Bifurcat. Chaos 24 1450082
|
[42] |
Gu H G, Ren W, Lu Q S, Wu S G and Chen W J 2001 Phys. Lett. A 285 63
|
[43] |
Hestrin S and Galarreta M 2005 Trends Neurosci. 28 304
|
[44] |
Chow C and Kopell N 2000 Neural Comput. 12 1643
|
[45] |
Wang H J, Huang H B and Qi G X 2005 Phys. Rev. E 72 037203
|
[46] |
Pikovsky A, Zaks M, Rosenblum M, Osipov G and Kurths J 1997 Chaos 7 680
|
[47] |
Chen J Y, Wong K W and Shuai J W 2002 Phys. Rev. E 66 056203
|
[48] |
Taherion S and Lai Y C 1999 Phys. Rev. E 59 6247
|
[49] |
Corron N J, Blakely J N and Pethel S D 2005 Chaos 15 023110
|
[50] |
Wu X and Ma J 2013 PLoS One 8 e55403
|
[51] |
Ma J, Huang L, Wang C N and Pu Z S 2013 Commun. Theor. Phys. 59 233
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|