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Investigation of emergence of target wave and spiral wave in neuronal network induced by gradient coupling

Xu Ying Wang Chun-Ni Jin Wu-Yin Ma Jun

Investigation of emergence of target wave and spiral wave in neuronal network induced by gradient coupling

Xu Ying, Wang Chun-Ni, Jin Wu-Yin, Ma Jun
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  • Distinct rhythm and self-organization in collective electric activities of neurons could be observed in a neuronal system composed of a large number of neurons. It is found that target wave can be induced in the network by imposing continuous local periodical force or introducing local heterogeneity in the network; and these target waves can regulate the wave propagation and development as pacemaker' in the network or media. A regular neuronal network is constructed in two-dimensional space, in which the local kinetics can be described by Hindmarsh-Rose neuron model, the emergence and development of ordered waves are investigated by introducing gradient coupling between neurons. For simplicity, the center area is selected by the largest coupling intensity, which is gradually decreased at certain step with increasing distance from the center area. It is found that the spiral wave and/or the target wave can be induced by appropriate selection of gradient coupling, and both waves can occupy the network, and then the collective behaviors of the network can be regulated to show ordered states. Particularly, the ordered wave can be effective to dominate the collective behavior of neuronal networks, even as the stochastic values are used for initial states. These results associated with the gradient coupling on the regulating collective behaviors could be useful to understand the self-organization behaviors in neuronal networks.
      Corresponding author: Ma Jun, hyperchaos@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11265008, 11365014).
    [1]

    Shilnikov S 2012 Nonlinear Dyn. SI 68 305

    [2]

    Rulkov N F 2002 Phys. Rev. E 65 041922

    [3]

    Storace M, Linaro D, de Lange E 2008 Chaos 18 033128

    [4]

    Huang X H, Hu G 2014 Chinese Phys. B 23 0108703

    [5]

    Wang M L, Wang J S 2015 Acta Phys. Sin. 64 108701(in Chinese) [王美丽, 王俊松 2015 物理学报 64 108701]

    [6]

    Jiang M, Zhu J, Liu Y P, Yang M P, Tian C P, Jiang S, Wang Y H, Guo H, Wang K Y, Shu Y S 2012 PLoS Biol. 10 e1001324

    [7]

    Morris C, Lecar H 1981 Biophys. J. 35 193

    [8]

    Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond B Biol. Sci. 221 87

    [9]

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

    [10]

    Zhang LS, Gu W F, Hu G, Mi Y Y 2014 Chinese Phys. B 23 0108902

    [11]

    Kitajima H, Yoshihara T 2012 Physica D 241 1804

    [12]

    Jia B 2014 Chin. Phys. B 23 050510

    [13]

    Storace M, Linaro D, de Lange E 2008 Chaos 18 033128

    [14]

    Wig G S, Schlaggar B L, Petersen S E 2011 Ann N. Y. Acad. Sci. 1224 126

    [15]

    Wang H X, Wang Q Y, Zheng Y H 2014 Sci. China Tech. Sci. 57 872

    [16]

    Torrealdea FJ, Sarasola C, d'Anjou A 2009 Chaos, Solitons Fract. 40 60

    [17]

    Yu L C, Liu L W 2014 Phys. Rev. E 89 032725

    [18]

    Wang R B, Zhang Z K, Qu J Y, Cao J T 2011 IEEE T. Neural. Networ. 22 1097

    [19]

    Ma J, Song X L, Jin W Y, Wang C N 2015 Chaos, Solition. Fract. 80 31

    [20]

    Jia B, Gu H G, Song S L 2013 Sci. China Phys. Mech. 43 518

    [21]

    Gu H G, Chen S G 2014 Sci. China Tech. Sci 57 864

    [22]

    Tang J, Luo J M, Ma J 2013 PLoS One 8 080324

    [23]

    Yu Y G, Liu F, Wang W 2001 Biol. Cybern. 84 227

    [24]

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

    [25]

    Perc M 2008 Phys. Rev. E 78 036105

    [26]

    Yılmaz E, Uzuntarla M, Ozer M, Perc M 2013 Physica A 392 5735

    [27]

    Zhang J Q, Wang C D, Wang M S, Huang S F 2011 Nerocomput. 74 2961

    [28]

    Wang Q Y, Zheng Y H, Ma J 2013 Chaos Solitons Fractals 56 19

    [29]

    Zeltser L M, Seeley R J, Tschoep M H 2012 Nature Neurosci. 15 1336

    [30]

    Elbasiouny Sherif M 2014 J. Appl. Physiol. 117 1243

    [31]

    Yang Z Q, Hao L J 2014 Sci. China Tech. Sci. 57 885

    [32]

    Wang Q Y, Chen G R, Perc M 2011 PLoS One 6 e15851

    [33]

    Xie Y, Kang Y M, Liu Y, Wu Y 2014 Sci. China Tech. Sci. 57 914

    [34]

    Jiao X F, Zhu D F 2014 Sci. China Tech. Sci. 57 923

    [35]

    Gu H G, Chen S G 2014 Sci. China Tech. Sci. 57 864

    [36]

    Qin H X, Wu Y, Wang C N, Ma J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 164

    [37]

    Sun X J, Shi X 2014 Sci. China Tech. Sci. 57 879

    [38]

    Baghdadi G, Jafari S, Sprott J C, Towhidkhah F, Hashemi Golpayegani M R 2015 Commun. Nonlinear Sci. Numer. Simulat. 20 174

    [39]

    Ren G D, Wu G, Ma J, Chen Y 2015 Acta Phys. Sin. 64 058702(in Chinese) [任国栋, 武刚, 马军, 陈旸 2015 物理学报 64 058702]

    [40]

    Qin H X, Ma J, Jin W Y, Wang C N 2014 Sci. China Tech. Sci. 57 936

    [41]

    Zhang L S, Liao X H, Mi Y Y, Qian Y, Hu G 2014 Chin. Phys. B 23 078906

    [42]

    Li J J, Wu Y, Du M M, Liu W M 2015 Acta Phys. Sin. 64 030503(in Chinese) [李佳佳, 吴莹, 独盟盟, 刘伟明 2015 物理学报 64 030503]

    [43]

    Ma J, Wang C N, Ying H P, Chu R T 2013 Sci. China Phys. Mech. Astro. 56 1126

    [44]

    Pan J T, Cai M C, Li B W, Zhang H 2013 Phys. Rev. E 87 062907

    [45]

    Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 89 022920

    [46]

    Li B W, Zhang H, Ying H P 2009 Phys. Rev. E 79 026220

    [47]

    Ma J, Wu Y, Wu N J, Guo H Y 2013 Sci. China Phys. Mech. Astro. 56 952

    [48]

    Ma J, Liu Q R, Ying H P, Wu Y 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1665

  • [1]

    Shilnikov S 2012 Nonlinear Dyn. SI 68 305

    [2]

    Rulkov N F 2002 Phys. Rev. E 65 041922

    [3]

    Storace M, Linaro D, de Lange E 2008 Chaos 18 033128

    [4]

    Huang X H, Hu G 2014 Chinese Phys. B 23 0108703

    [5]

    Wang M L, Wang J S 2015 Acta Phys. Sin. 64 108701(in Chinese) [王美丽, 王俊松 2015 物理学报 64 108701]

    [6]

    Jiang M, Zhu J, Liu Y P, Yang M P, Tian C P, Jiang S, Wang Y H, Guo H, Wang K Y, Shu Y S 2012 PLoS Biol. 10 e1001324

    [7]

    Morris C, Lecar H 1981 Biophys. J. 35 193

    [8]

    Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond B Biol. Sci. 221 87

    [9]

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

    [10]

    Zhang LS, Gu W F, Hu G, Mi Y Y 2014 Chinese Phys. B 23 0108902

    [11]

    Kitajima H, Yoshihara T 2012 Physica D 241 1804

    [12]

    Jia B 2014 Chin. Phys. B 23 050510

    [13]

    Storace M, Linaro D, de Lange E 2008 Chaos 18 033128

    [14]

    Wig G S, Schlaggar B L, Petersen S E 2011 Ann N. Y. Acad. Sci. 1224 126

    [15]

    Wang H X, Wang Q Y, Zheng Y H 2014 Sci. China Tech. Sci. 57 872

    [16]

    Torrealdea FJ, Sarasola C, d'Anjou A 2009 Chaos, Solitons Fract. 40 60

    [17]

    Yu L C, Liu L W 2014 Phys. Rev. E 89 032725

    [18]

    Wang R B, Zhang Z K, Qu J Y, Cao J T 2011 IEEE T. Neural. Networ. 22 1097

    [19]

    Ma J, Song X L, Jin W Y, Wang C N 2015 Chaos, Solition. Fract. 80 31

    [20]

    Jia B, Gu H G, Song S L 2013 Sci. China Phys. Mech. 43 518

    [21]

    Gu H G, Chen S G 2014 Sci. China Tech. Sci 57 864

    [22]

    Tang J, Luo J M, Ma J 2013 PLoS One 8 080324

    [23]

    Yu Y G, Liu F, Wang W 2001 Biol. Cybern. 84 227

    [24]

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

    [25]

    Perc M 2008 Phys. Rev. E 78 036105

    [26]

    Yılmaz E, Uzuntarla M, Ozer M, Perc M 2013 Physica A 392 5735

    [27]

    Zhang J Q, Wang C D, Wang M S, Huang S F 2011 Nerocomput. 74 2961

    [28]

    Wang Q Y, Zheng Y H, Ma J 2013 Chaos Solitons Fractals 56 19

    [29]

    Zeltser L M, Seeley R J, Tschoep M H 2012 Nature Neurosci. 15 1336

    [30]

    Elbasiouny Sherif M 2014 J. Appl. Physiol. 117 1243

    [31]

    Yang Z Q, Hao L J 2014 Sci. China Tech. Sci. 57 885

    [32]

    Wang Q Y, Chen G R, Perc M 2011 PLoS One 6 e15851

    [33]

    Xie Y, Kang Y M, Liu Y, Wu Y 2014 Sci. China Tech. Sci. 57 914

    [34]

    Jiao X F, Zhu D F 2014 Sci. China Tech. Sci. 57 923

    [35]

    Gu H G, Chen S G 2014 Sci. China Tech. Sci. 57 864

    [36]

    Qin H X, Wu Y, Wang C N, Ma J 2015 Commun. Nonlinear Sci. Numer. Simulat. 23 164

    [37]

    Sun X J, Shi X 2014 Sci. China Tech. Sci. 57 879

    [38]

    Baghdadi G, Jafari S, Sprott J C, Towhidkhah F, Hashemi Golpayegani M R 2015 Commun. Nonlinear Sci. Numer. Simulat. 20 174

    [39]

    Ren G D, Wu G, Ma J, Chen Y 2015 Acta Phys. Sin. 64 058702(in Chinese) [任国栋, 武刚, 马军, 陈旸 2015 物理学报 64 058702]

    [40]

    Qin H X, Ma J, Jin W Y, Wang C N 2014 Sci. China Tech. Sci. 57 936

    [41]

    Zhang L S, Liao X H, Mi Y Y, Qian Y, Hu G 2014 Chin. Phys. B 23 078906

    [42]

    Li J J, Wu Y, Du M M, Liu W M 2015 Acta Phys. Sin. 64 030503(in Chinese) [李佳佳, 吴莹, 独盟盟, 刘伟明 2015 物理学报 64 030503]

    [43]

    Ma J, Wang C N, Ying H P, Chu R T 2013 Sci. China Phys. Mech. Astro. 56 1126

    [44]

    Pan J T, Cai M C, Li B W, Zhang H 2013 Phys. Rev. E 87 062907

    [45]

    Gao X, Zhang H, Zykov V, Bodenschatz E 2014 New J. Phys. 89 022920

    [46]

    Li B W, Zhang H, Ying H P 2009 Phys. Rev. E 79 026220

    [47]

    Ma J, Wu Y, Wu N J, Guo H Y 2013 Sci. China Phys. Mech. Astro. 56 952

    [48]

    Ma J, Liu Q R, Ying H P, Wu Y 2013 Commun. Nonlinear Sci. Numer. Simulat. 18 1665

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Publishing process
  • Received Date:  20 April 2015
  • Accepted Date:  04 June 2015
  • Published Online:  05 October 2015

Investigation of emergence of target wave and spiral wave in neuronal network induced by gradient coupling

    Corresponding author: Ma Jun, hyperchaos@163.com
  • 1. Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China;
  • 2. College of Mechano-Electronic Engineering, University of Technology, Lanzhou 730050, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11265008, 11365014).

Abstract: Distinct rhythm and self-organization in collective electric activities of neurons could be observed in a neuronal system composed of a large number of neurons. It is found that target wave can be induced in the network by imposing continuous local periodical force or introducing local heterogeneity in the network; and these target waves can regulate the wave propagation and development as pacemaker' in the network or media. A regular neuronal network is constructed in two-dimensional space, in which the local kinetics can be described by Hindmarsh-Rose neuron model, the emergence and development of ordered waves are investigated by introducing gradient coupling between neurons. For simplicity, the center area is selected by the largest coupling intensity, which is gradually decreased at certain step with increasing distance from the center area. It is found that the spiral wave and/or the target wave can be induced by appropriate selection of gradient coupling, and both waves can occupy the network, and then the collective behaviors of the network can be regulated to show ordered states. Particularly, the ordered wave can be effective to dominate the collective behavior of neuronal networks, even as the stochastic values are used for initial states. These results associated with the gradient coupling on the regulating collective behaviors could be useful to understand the self-organization behaviors in neuronal networks.

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