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实际神经元网络中，信息传递时电突触和化学突触同时存在，并且有些神经元间的时滞很小可以忽略.本文构建了带有不同类型突触耦合的小世界网络，研究部分时滞、混合突触及噪声对随机共振的影响.结果表明：兴奋性和抑制性突触的比例影响共振的产生；在抑制性突触为主的网络里，几乎不产生随机共振.系统最佳噪声强度和化学突触比例大致呈线性递增关系；特别是在以化学耦合为主的混合突触网络里，仅当兴奋性突触与抑制性突触比例约为4：1时，噪声才可诱导网络产生共振行为.在此比例下，引入部分时滞发现时滞可诱导网络产生随机多共振，且随网络中时滞边比例的增加，系统响应强度达到最优水平的时滞取值区间逐渐变窄；同时发现，网络中含有的化学突触越多，部分时滞诱导产生的多共振行为越强.此外，当时滞为系统固有周期的整数倍时，时滞越大共振所对应的噪声区域越广；并且网络中时滞边越多，越容易促使噪声和时滞诱导其产生明显的共振行为.In real neuronal systems, information transition delay is an inevitable factor. However, between some neurons, neuronal information is transmitted instantaneously or the time delay is too small and can be neglected. Thus, differing from the conventional studies where all connections are considered to be delayed, here we mainly focus on the effect of partial time delay on stochastic resonance in a Watts-Strogatz small-world neuronal network. Meanwhile, in the same neuronal network, the electrical and chemical synapses usually coexist. Thus, effects of hybrid synapses are also considered. Firstly, in the absence of time delay, noise could induce stochastic resonance when the neuronal network contains much more excitatory synapses than inhibitory ones; while it cannot induce stochastic resonance vise verse. Interestingly, it is further revealed that when the ratio of excitatory synapse to inhibitory synapse is approximately 4:1, noise-induced stochastic resonance is more robust. Thus, to discuss the effects of other factors on noise-induced stochastic resonance, we set this ratio to be 4:1. In the absence of time delay, we also consider effects of chemical synapses with a ratio of excitatory synapse to inhibitory synapse of 4:1 on the noise-induced stochastic resonance. The obtained results show that the noise could always induce stochastic resonance no matter how the probability of chemical synapses varies. And the optimal noise intensity increases linearly with the probability of chemical synapses increasing. For partial time delay, it is surprisingly found that the stochastic resonance could appear multiple times with the variation of the time delay being just for small partial time delay probability. Moreover, chemical synapse is found to facilitate this effect of partial time delay. Finally, by analyzing the joint effects of partial time delay and noise intensity, it is found that the larger the time delay and the partial time delay probability are, the wider the optimal noise region corresponding to large response amplitude is.
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Keywords:
- stochastic resonance /
- hybrid synapses /
- partial time delay
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[1] Longtin A, Bulsara A, Moss F 1991 Phys. Rev. Lett. 67 656
[2] Mori T, Kai S 2002 Phys. Rev. Lett. 88 218101
[3] Wang Q Y, Shi X, Lu Q S 2008 Synchronization Dynamics in the Coupled System of Neurons (Beijing: Science Press) p99 (in Chinese) [王青云, 石霞, 陆启韶 2008 神经元耦合系统的同步动力学 (北京: 科学出版社) 第99页]
[4] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453
[5] Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[6] Hanggi P 2002 ChemPhysChem 3 285
[7] Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130
[8] Sun X J, Perc M, Lu Q, Kurths J 2008 Chaos 18 023102
[9] Sun X J, Lu Q S 2014 Chin. Phys. Lett. 31 020502
[10] Zhou C S, Kurths J, Hu B 2001 Phys. Rev. Lett. 87 098101
[11] Zhou X R, Luo X S 2008 Acta Phys. Sin. 57 2849 (in Chinese) [周小荣, 罗晓曙 2008 57 2849]
[12] Wang M S, Hou Z H, Xin H W 2006 Chin. Phys. 23 2666
[13] Lin X, Gong Y B, Wang L 2011 Chaos 21 043109
[14] Ozer M, Perc M, Uzuntarla M 2009 Phys. Lett. A 373 964
[15] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010 Physica A 389 2642
[16] Tessone C J, Mirasso C R, Torah R, Gunton J D 2006 Phys. Rev. Lett. 97 194101
[17] Li Y Y, Jia B, Gu H G, An S C 2012 Commun. Theor. Phys. 57 817
[18] Perc M 2007 Phys. Rev. E 76 066203
[19] Sudhof T C, Malenka R C 2008 Neuron 60 469
[20] Connors B W, Long M A 2004 Annu. Rev. Neurosci. 27 393
[21] Shi X, Wang Q, Lu Q 2008 Cogn. Neurodynamics 2 195
[22] Wang Q, Zhang H, Chen G 2012 Chaos 22 043123
[23] de Zeeuw C I, Holstege J C, Ruigrok T J H, Voogd J 1990 Neuroscience 34 645
[24] de Zeeuw C I, Hoogenraad C C, Koekkoek S K E, Ruigrok T J, Galjart N, Simpson J I 1998 Trends. Neurosci. 21 391
[25] Kopell N, Ermentrout B 2004 Proc. Natl. Acad. Sci. USA 101 15482
[26] Yilmaz E, Uzuntarla M, Ozer M, Perc M 2013 Physica A 392 5735
[27] Yu H, Guo X, Wang J 2017 Commun. Nonlinear Sci. 42 532
[28] Turrigiano G G, Nelson S B 2004 Nat. Rev. Neurosci. 5 97
[29] Wang Y, Sugita S, Sudhof T C, Biol J 2000 J. Biol. Chem. 275 20033
[30] Bckers J, Wildanger D, Vicidomini G, Kastrup L, Hell S W 2011 Opt. Express 19 3130
[31] Turrigiano G G, Nelson S B 2000 Curr. Opin. Neurobiol. 10 358
[32] Vogels T P, Sprekeler H, Zenke F, Clopath C, Gerstner W 2011 Science 334 1569
[33] Eichler S A, Meier J C 2008 Front. Mol. Neurosci. 1 PMC2526001
[34] Petrou M, Pop-Busui R, Foerster B R, Edden R A, Callaghan B C, Harte S E, Harris R E, Clauw D J, Feldman E L 2012 Acad. Radiol. 19 607
[35] Malina K C K, Jubran M, Katz Y, Lampl I J 2013 J. Neurosci. 33 8463
[36] Wang M L, Wang J S 2015 Acta Phys. Sin. 64 108701 (in Chinese) [王美丽, 王俊松 2015 64 108701]
[37] Gosak M, Markovic R, Marhl M 2012 Physica A 391 2764
[38] Wang Q, Perc M, Duan Z, Chen G 2009 Chaos 19 023112
[39] Yu H, Wang J, Liu C, Deng B, Wei X 2014 Physica A 405 25
[40] Sun X J, Li G F 2016 Acta Phys. Sin. 65 120502 (in Chinese) [孙晓娟, 李国芳 2016 65 120502]
[41] Sun X, Li G 2017 Nonlinear Dynam. 89 1
[42] Sun X, Perc M, Kurths J 2017 Chaos 27 053113
[43] Rulkov N F 2001 Phys. Rev. Lett. 86 183
[44] Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433
[45] Zaikin U A, García-Ojalvo J, Báscones R, Kurths J 2003 Phys. Lett. A 312 348
[46] Watts D J, Strogatz S H 1998 Nature 393 440
[47] Watt A J, Desai N S 2010 Front. Synaptic. Neurosci. 2 PMC3059670
[48] Song S, Miller K D, Abbott L F 2000 Nat. Neurosci. 3 919
[49] Toyoizumi T, Pfister J P, Aihara K, Gerstner W 2007 Neural. Comput. 19 639
[50] Hilgetag C C, Burns G A P C, OŃeill M A, Scannell J W, Young M P 2000 Philos. Trans. Roy. Soc. B 355 91
[51] Hilgetag C C, Kaiser M 2004 Neuroinformatics 2 353
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