Synchronization in the Uncoupled Neuron System
ZHANG Ji-Qian** , HUANG Shou-Fang, PANG Si-Tao, WANG Mao-Sheng, GAO Sheng
College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000
Abstract :Using the model of Hindmarsh–Rose neurons, we study the synchronous behavior of the firing patterns in an uncoupled cell system. In this work, the membrane current Iext is selected as a controllable parameter, whose initial values for all N cells are set to be near one of the bifurcation points randomly. It is found that the system will show un-synchronous state when the external stimuli is absent, otherwise, full synchrony will appear, even though without any coupling connection among these N neurons, indicating the occurrence of uncoupled synchrony. Moreover, similar behavior could also be observed when these neurons are set to be near other bifurcation points. The synchronous error is calculated for discussing this uncoupled synchrony behavior. Finally, we find that such synchrony may have some inherent relevance with the decrease of phase difference between different cells. Our results suggest that biological neuron systems may achieve an effective response to external feeble stimulus by the mode of uncoupled synchrony instead of only by the coupled scheme.
收稿日期: 2015-09-06
出版日期: 2016-01-05
:
05.45.Xt
(Synchronization; coupled oscillators)
05.40.-a
(Fluctuation phenomena, random processes, noise, and Brownian motion)
68.35.Rh
(Phase transitions and critical phenomena)
87.17.Aa
(Modeling, computer simulation of cell processes)
87.15.Zg
(Phase transitions)
[1] Brette R 2012 PLoS Comput. Biol. 8 e1002561 [2] Toutounji H and Pipa G 2014 PLoS Comput. Biol. 10 e1003512 [3] Gong Y B, Lin X, Wang L and Hao Y H 2011 Sci. Chin. Chem. 54 1498 [4] Liang L S, Zhang J Q, Liu L Z and Huang S F 2014 Chin. Phys. Lett. 31 050502 [5] Wang M S, Sun R Z, Huang W X, Tu Y B and Zhang J Q 2013 Commun. Theor. Phys. 60 545 [6] Zou Y Y and Li H H 2014 Chin. Phys. Lett. 31 100501 [7] Zhou J, Wu X Q, Yu W W, Small M and Lu J A 2008 Chaos 18 043111 [8] Qin H X, Ma J, Jin W Y and Wang C N 2014 Commun. Theor. Phys. 62 755 [9] Wiessenfeld K, Colet P and Strogatz S H 1996 Phys. Rev. Lett. 76 404 [10] Engel A K, Kreiter A K, Konig P and Singer W 1991 Proc. Natl. Acad. Sci. USA 88 6048 [11] Jouaville L S, Ichas F, Holmuhamedov E L and Mazat J P 1995 Nature 377 438 [12] Wang Q Y, Chen G R and Perc M 2011 PLoS ONE 6 e15851 [13] Gómez G J, Zamora L G, Moreno Y and Arenas A 2010 PLoS ONE 5 e12313 [14] Nicolelis M A L, Baccala L A, Lin R C S and Chapin J K 1995 Science 268 1353 [15] Uhlhaas P J and Singer W 2006 Neuron 52 155 [16] Hu B and Zhou C S 2000 Phys. Rev. E 61 R1001 [17] Buehlmann A and Deco G 2010 PLoS Comput. Biol. 6 e1000934 [18] Wang M S, Hou Z H and Xin H W 2006 ChemPhysChem 7 579 [19] Perc M 2009 Biophys. Chem. 141 175 [20] Memmesheimer R M and Timme M 2012 PLoS Comput. Biol. 8 e1002384 [21] Zhang J Q, Chen H S and Wang M S 2008 Commun. Theor. Phys. 50 903 [22] Ma J, Qin H X, Song X L and Chu R 2015 Int. J. Mod. Phys. B 29 1450239 [23] Shrii M M, Senthilkumar D V and Kurths J 2012 Europhys. Lett. 98 10003 [24] Tang J, Ma J, Yi M, Xia H and Yang X Q 2011 Phys. Rev. E 83 046207 [25] Wang Q Y, Duan Z S, Perc M and Chen G R 2008 Europhys. Lett. 83 50008 [26] Zhang J Q, Wang C D, Wang M S and Huang S F 2011 Neurocomputing 74 2961 [27] Wei D Q, Luo X S and Qin Y H 2008 Physica A 387 2155 [28] Batista C A S, Viana R L, Ferrari F A S, Lopes S R, Batista A M and Coninck J C P 2013 Phys. Rev. E 87 042713 [29] Chen H S, He G, Huang F and Hou Z H 2013 Chaos 23 033124 [30] Gray C M, Koening P and Engel A K 1989 Nature 338 334 [31] He D H, Shi P and Stone L 2003 Phys. Rev. E 67 027201 [32] Wu Y, Xu J X, Jin W Y and Hong L 2007 Chin. Phys. Lett. 24 3066 [33] Nakao H, Arai K and Kawamura Y 2007 Phys. Rev. Lett. 98 184101 [34] Hindmarsh J L and Rose R M 1994 Philos. Trans. R. Soc. B 346 129
[1]
. [J]. 中国物理快报, 2020, 37(1): 14501-014501.
[2]
. [J]. 中国物理快报, 2016, 33(12): 120501-120501.
[3]
. [J]. 中国物理快报, 2016, 33(07): 70501-070501.
[4]
. [J]. 中国物理快报, 2016, 33(05): 50501-050501.
[5]
. [J]. 中国物理快报, 2016, 33(05): 50502-050502.
[6]
. [J]. 中国物理快报, 2015, 32(12): 128901-128901.
[7]
. [J]. 中国物理快报, 2015, 32(11): 110502-110502.
[8]
. [J]. 中国物理快报, 2015, 32(11): 110503-110503.
[9]
. [J]. 中国物理快报, 2015, 32(06): 60502-060502.
[10]
. [J]. 中国物理快报, 2015, 32(4): 40502-040502.
[11]
. [J]. 中国物理快报, 2015, 32(03): 30502-030502.
[12]
. [J]. 中国物理快报, 2015, 32(01): 10502-010502.
[13]
. [J]. 中国物理快报, 2015, 32(01): 10503-010503.
[14]
. [J]. 中国物理快报, 2014, 31(10): 100501-100501.
[15]
. [J]. 中国物理快报, 2014, 31(08): 80503-080503.