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部分时滞诱发Watts-Strogatz小世界神经元网络产生随机多共振

孙晓娟 李国芳

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部分时滞诱发Watts-Strogatz小世界神经元网络产生随机多共振

孙晓娟, 李国芳

Stochastic multi-resonance induced by partial time delay in a Watts-Strogatz small-world neuronal network

Sun Xiao-Juan, Li Guo-Fang
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  • 已有研究显示时滞可诱发神经元网络产生随机多共振, 但它们主要讨论了神经元间的耦合都存在时滞的情形. 然而实际中, 有些神经元间的信息传递是瞬时的或时滞很小可以忽略的, 即神经元网络中只有部分神经元间的耦合具有时滞, 简称部分时滞(若神经元网络内共有l条耦合边, 其中有l1条耦合边是具有时滞的, 而剩余的耦合边的时滞为零, 则我们称这类时滞为部分时滞). 本文以Watts-Strogatz小世界神经元网络为研究对象, 主要讨论部分时滞对该神经元网络系统响应强度的影响. 研究结果指出, 系统响应强度随部分时滞的增加呈现多峰的变化态势, 即部分时滞可诱发随机多共振现象; 而且使系统响应强度达到最优水平的部分时滞的取值区间随随机时滞边概率的增加渐渐变窄, 当随机时滞边概率足够大时, 系统响应强度只有在时滞位于外界信号周期的整数倍附近才会达到最优. 此外, 我们还分析了随机连边概率和神经元网络中边的总数对部分时滞诱发的随机多共振现象的影响. 结果显示, 部分时滞诱发的随机多共振现象对随机连边概率具有一定的鲁棒性, 而神经元网络中边的总数对部分时滞诱发的随机多共振的影响则较大.
    In a neuronal system, propagation speed of neuronal information is mainly determined by the length, the diameter, and the kind of the axons between the neurons. Thus, some communications between neurons are not instantaneous, and others are instantaneous or with some negligible delay. In the past years, effects of time delay on neuronal dynamics, such as synchronization, stochastic resonance, firing regularity, etc., have been investigated. For stochastic resonance, it has been reported recently that stochastic multi-resonance in a neuronal system can be induced by time delay. However, in these studies, time delay has been introduced to every connection of the neuronal system. As mentioned in the beginning, in a real neuronal system, communication between some neurons can be instantaneous or with some negligible delays. Thus, considering the effect of partial time delay (time delay is called as partial time delay if only part of connections are delayed) on neuronal dynamics could be more meaningful.In this paper, we focus on discussing effect of partial time delay on response amplitude of a Watts-Strogatz neuronal network which is locally modeled by Rulkov map. With the numerically obtained results, we can see that partial time delay can induce a stochastic multi-resonance which is indicated by the multi-peak characteristics in the variation of response amplitude with partial time delay. Namely, partial time delay could also induce stochastic multi-resonance in a neuronal system. Moreover, we also find that optimal response amplitude can be reached in much wider range of the partial time delay value when delayed connections are less (i.e., the partial time delay probability is small). This is different from the case in which all connections are delayed, where response amplitude become optimal only when time delay is nearly the multiples of external signal's period. But the range of the partial time delay value becomes narrower and narrower with the increasing of the partial time delay probability and when the partial time delay probability is large enough, response amplitude becomes optimal only when time delay is nearly the multiples of external signal period. It is similar to the case where all connections are delayed. Furthermore, effects of random rewiring probability and total link number in the neuronal network on partial time delay induced stochastic multi-resonance are also studied. It is found that partial time delay induced stochastic multi-resonance is robust to random rewiring probability but not robust to total link number. Stochastic resonance is a very important nonlinear phenomenon in neuroscience, thus, our obtained results could have some implications in this field.
      通信作者: 孙晓娟, sunxiaojuan@bupt.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 11102094, 11472061, 11572084)资助的课题.
      Corresponding author: Sun Xiao-Juan, sunxiaojuan@bupt.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11102094, 11472061, 11572084).
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    Zhao Z G, Gu H G 2015 Chaos, Solitions Fractals 80 96

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    Gu H G 2015 PLoS One 10 e0138593

  • [1]

    Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A: Math. Gen. 14 L453

    [2]

    Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775

    [3]

    Masoliver J, Robinson A, Weiss G H 1995 Phys. Rev. E 51 4021

    [4]

    Porra J M 1997 Phys. Rev. E 55 6533

    [5]

    Collins J J, Chow C C, Capela A C, Imhoff T T 1996 Phys. Rev. E 54 5575

    [6]

    Collins J J, Chow C C, Imhoff T T 1995 Phys. Rev. E 52 R3321

    [7]

    Heneghan C, Chow C C, Collins J J, Imhoff T T, Lowen S B, Teich M C 1996 Phys. Rev. E 54 R2228

    [8]

    Vilar J M G, Rub J M 1997 Phys. Rev. Lett. 78 2882

    [9]

    Longtin A, Bulsara A, Moss F 1991 Phys. Rev. Lett. 67 656

    [10]

    Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365 337

    [11]

    Sun Z K, Lu P J, Xu W 2014 Acta Phys. Sin. 63 220503 (in Chinese) [孙中奎, 鲁捧菊, 徐伟 2014 物理学报 63 220503]

    [12]

    Jin Y F 2015 Chin. Phys. B 24 110501

    [13]

    Xu Y, Wu J, Zhang H Q, Ma S J 2012 Nonlinear Dyn. 70 531

    [14]

    Gammaitoni L, Hnggi P, Jung P 1998 Rev. Mod. Phys. 70 223

    [15]

    Lindner B, Garcia-Ojalvo J, Neiman A, Schimansky-Geier L 2004 Phys. Rep. 392 321

    [16]

    Perc M 2007 Phys. Rev. E 76 066203

    [17]

    Sun X J, Perc M, Lu Q S, Kurths J 2008 Chaos 18 023102

    [18]

    Sun X J, Lu Q S 2014 Chin. Phys. Lett. 31 020502

    [19]

    Qin H X, Ma J, Wang C N, Wu Y 2014 PLoS One 9 e100849

    [20]

    Gu H G, Jia B, Li Y Y, Chen G R 2013 Physica A 392 1361

    [21]

    Yu H T, Guo X M, Wang J, Deng B, Wei X L 2015 Physica A 419 307

    [22]

    Volkov E I, Ullner E, Kurths J 2005 Chaos 15 023105

    [23]

    Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010 Physica A 389 2642

    [24]

    Lin X, Gong Y B, Wang L 2011 Chaos 21 043109

    [25]

    Jia Y B, Gu H G 2015 Chaos 25 123124

    [26]

    Wang Q Y, Zhang H H, Perc M, Chen G R 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3979

    [27]

    Wang Q Y, Perc M, Duan Z S, Chen G R 2009 Chaos 19 023112

    [28]

    Hao Y H, Gong Y B, Lin X 2011 Neurocomputing 74 1748

    [29]

    Rulkov N F 2001 Phys. Rev. Lett. 86 183

    [30]

    Ibarz B, Casado J M, Sanjuan M A F 2011 Phys. Rep. 501 1

    [31]

    Hilborn R C 2004 Am. J. Phys. 72 528

    [32]

    Rulkov N F, Timofeev I, Bazhenov M 2004 J. Comput. Neurosci. 17 203

    [33]

    Rulkov N F, Bazhenov M 2008 J. Biol. Phys. 34 279

    [34]

    Nowotny T, Huerta R, Abarbanel H D I, Rabinovich M I 2005 Biol. Cybern. 93 436

    [35]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [36]

    Landa P S, McClintock P V E 2000 J. Phys. A: Math. Gen. 33 L433

    [37]

    Zaikin U A, Garca-Ojalvo J, Bscones R, Kurths J 2003 Phys. Lett. A 312 348

    [38]

    Rajasekar S, Used J, Wagemakers A, Sanjuan M A F 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3435

    [39]

    Zhao Z G, Gu H G 2015 Chaos, Solitions Fractals 80 96

    [40]

    Gu H G 2015 PLoS One 10 e0138593

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出版历程
  • 收稿日期:  2016-02-02
  • 修回日期:  2016-04-08
  • 刊出日期:  2016-06-05

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