Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons

Wang Peng Li Qian-Yun Tang Guo-Ning

Wang Peng, Li Qian-Yun, Tang Guo-Ning. Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons. Acta Phys. Sin., 2018, 67(3): 030502. doi: 10.7498/aps.67.20172140
Citation: Wang Peng, Li Qian-Yun, Tang Guo-Ning. Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons. Acta Phys. Sin., 2018, 67(3): 030502. doi: 10.7498/aps.67.20172140

Spontaneous generation of spiral wave in the array of Hindmarsh-Rose neurons

Wang Peng, Li Qian-Yun, Tang Guo-Ning
PDF
Get Citation

(PLEASE TRANSLATE TO ENGLISH

BY GOOGLE TRANSLATE IF NEEDED.)

  • Spiral waves have been reported to be existent in the neocortex, during pharmacologically induced oscillations and sleep-like states. In the last decades, theoretical studies have demonstrated an underlying mechanism of the generation of spiral waves in a heart system. Nevertheless, how can a neural system produce spontaneous spiral wave and whether this behavior is sensitive to the dynamics of isolated neurons have not been systematically studied yet. In this paper we propose a modified Hindmarsh-Rose (HR) neuron model to study whether spiral wave can occur spontaneously in a two-dimensional array of HR neurons, which evolves from the initial state with a random phase distribution. The simulation results show that whether spiral wave can occur spontaneously in the system depends on the state of the single HR neuron, initial state of system and coupling strength. Especially, the state of the single HR neuron plays a central role. When the single HR neuron is in the state of period 1 spike, multiple spiral waves and spiral pairs can be generated spontaneously in the system for a certain range of coupling strength. In this case, the formations of spiral waves are completely independent of the initial state of the system, and as long as choosing an appropriate coupling strength, a single spiral wave can be found in the system. Furthermore, when the coupling strength exceeds a certain threshold value, the system will exhibit three kinds of dynamical behaviors, and correspond to three kinds of the different initial states, respectively. When system evolves from the first kind of initial state, the single spiral wave can be found occasionally in the system. When the system evolves from the second or third kind of initial state, the oscillation with intermittently global synchronization and oscillation death can be observed in the system, respectively. When a single HR neuron is in the state of period 2 spike, the spiral wave can appear spontaneously in the system only when the phase distribution of the initial state approaches to a uniform distribution. Moreover, the range of coupling strength on the generation of spiral wave is smaller than that of period 1 spike. When the single HR neuron is in a higher periodic state, it is difficult to generate spontaneously spiral wave in the system. These results are useful in understanding the spontaneous generation of spiral waves in the neocortex.
      PACS:
      05.45.Xt(Synchronization; coupled oscillators)
      82.40.Ck(Pattern formation in reactions with diffusion, flow and heat transfer)
      89.75.Kd(Patterns)
      Corresponding author: Tang Guo-Ning, tangguoning@sohu.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11565005, 11365003, 11747307).
    [1]

    Winfree A T 1972 Science 175 634

    [2]

    Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825

    [3]

    Plapp B P, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334

    [4]

    Mller S C, Plesser T, Hess B 1985 Science 230 661

    [5]

    Vanag V K, Epstein I R 2001 Science 294 835

    [6]

    Foerster P, Mller S C, Hess B 1990 Development 109 11

    [7]

    Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349

    [8]

    Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978

    [9]

    Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S T, Wu J Y 2004 J. Neurosci. 24 9897

    [10]

    Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202

    [11]

    Chen J X, Guo M M, Ma J 2016 Europhys. Lett. 113 38004

    [12]

    Chen J X, Liang P, Zheng Q, Zhao Y H, Ying H P 2014 Chaos 24 033103

    [13]

    Pumir A, Nikolski V, Horning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101

    [14]

    Gan Z N, Cheng X M 2010 Chin. Phys. B 19 050514

    [15]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S 2011 Nat Neurosci. 14 1599

    [16]

    Jung P, Cornell-Bell A, Madden K S, Moss F 1998 J. Neurophysiol. 79 1098

    [17]

    Garca-Ojalvo J, Schimansky-Geier L 1999 Europhys. Lett. 47 298

    [18]

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

    [19]

    Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504

    [20]

    Wang Q Y, Perc M, Duan Z, Chen G 2008 Phys. Lett. A 372 5681

    [21]

    Jung P, Cornell-Bell A, Moss F, Kadar S, Wang J, Showalter K 1998 Chaos 8 567

    [22]

    Ullner E, Zaikin A, Garca-Ojalvo J, Kurths J 2003 Phys. Rev. Lett. 91 180601

    [23]

    Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151

    [24]

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

    [25]

    Jiruska P, De-Curtis M, Jefferys J G R, Schevon C A, Schiff S J, Schindler K 2013 J. Physiol. 591 787

    期刊类型引用(3)

    1. 赵松,刘丹,罗小元,袁毅. 经颅磁声刺激下分数阶扩展Hindmarsh-Rose神经元放电特性分析. 电子与信息学报. 2022(02): 534-542 . 百度学术
    2. 汪芃,李倩昀,黄志精,唐国宁. 在兴奋-抑制混沌神经元网络中有序波的自发形成. 物理学报. 2018(17): 65-72 . 百度学术
    3. 倪之玮,李新政,白占国,李燕. 反应扩散系统中反螺旋波与反靶波的数值研究. 物理学报. 2018(18): 316-325 . 百度学术

    其他类型引用(2)

  • [1]

    Winfree A T 1972 Science 175 634

    [2]

    Larionova Y, Egorov O, Cabrera-Granado E, Esteban-Martin A 2005 Phys. Rev. A 72 033825

    [3]

    Plapp B P, Egolf D A, Bodenschatz E, Pesch W 1998 Phys. Rev. Lett. 81 5334

    [4]

    Mller S C, Plesser T, Hess B 1985 Science 230 661

    [5]

    Vanag V K, Epstein I R 2001 Science 294 835

    [6]

    Foerster P, Mller S C, Hess B 1990 Development 109 11

    [7]

    Davidenko J M, Pertsov A V, Salomonsz, Baxter W, Jalife J 1992 Nature 355 349

    [8]

    Huang X, Xu W, Liang J, Takagaki K, Gao X, Wu J 2010 Neuron 68 978

    [9]

    Huang X, Troy W C, Yang Q, Ma H, Laing C R, Schiff S T, Wu J Y 2004 J. Neurosci. 24 9897

    [10]

    Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simulat. 54 202

    [11]

    Chen J X, Guo M M, Ma J 2016 Europhys. Lett. 113 38004

    [12]

    Chen J X, Liang P, Zheng Q, Zhao Y H, Ying H P 2014 Chaos 24 033103

    [13]

    Pumir A, Nikolski V, Horning M, Isomura A, Agladze K, Yoshikawa K, Gilmour R, Bodenschatz E, Krinsky V 2007 Phys. Rev. Lett. 99 208101

    [14]

    Gan Z N, Cheng X M 2010 Chin. Phys. B 19 050514

    [15]

    Viventi J, Kim D H, Vigeland L, Frechette E S, Blanco J A, Kim Y S 2011 Nat Neurosci. 14 1599

    [16]

    Jung P, Cornell-Bell A, Madden K S, Moss F 1998 J. Neurophysiol. 79 1098

    [17]

    Garca-Ojalvo J, Schimansky-Geier L 1999 Europhys. Lett. 47 298

    [18]

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

    [19]

    Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504

    [20]

    Wang Q Y, Perc M, Duan Z, Chen G 2008 Phys. Lett. A 372 5681

    [21]

    Jung P, Cornell-Bell A, Moss F, Kadar S, Wang J, Showalter K 1998 Chaos 8 567

    [22]

    Ullner E, Zaikin A, Garca-Ojalvo J, Kurths J 2003 Phys. Rev. Lett. 91 180601

    [23]

    Ma J, Wu Y, Ying H P, Jia Y 2011 Chin. Sci. Bull. 56 151

    [24]

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

    [25]

    Jiruska P, De-Curtis M, Jefferys J G R, Schevon C A, Schiff S J, Schindler K 2013 J. Physiol. 591 787

  • [1] Huang Zhi-Jing, Li Qian-Yun, Bai Jing, Tang Guo-Ning. Entropy measurement of ordered patterns in neuronal network with repulsive coupling. Acta Physica Sinica, 2019, 68(11): 110503. doi: 10.7498/aps.68.20190231
    [2] Wang Peng, Li Qian-Yun, Huang Zhi-Jing, Tang Guo-Ning. Spontaneous formation of ordered waves in chaotic neuronal network with excitory-inhibitory connections. Acta Physica Sinica, 2018, 67(17): 170501. doi: 10.7498/aps.67.20180506
    [3] Qiao Xiao-Fen, Li Xiao-Li, Liu He-Nan, Shi Wei, Liu Xue-Lu, Wu Jiang-Bin, Tan Ping-Heng. Periodic oscillation in the reflection and photoluminescence spectra of suspended two-dimensional crystal flakes. Acta Physica Sinica, 2016, 65(13): 136801. doi: 10.7498/aps.65.136801
    [4] 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. Acta Physica Sinica, 2015, 64(19): 198701. doi: 10.7498/aps.64.198701
    [5] Zeng Guo, Li Xing-Yuan, Liu Tian-Qi, Zhao Rui. Multi-channel wide area adaptive damping control for suppressing low-frequency and sub-synchronous oscillation. Acta Physica Sinica, 2014, 63(22): 228801. doi: 10.7498/aps.63.228801
    [6] Chen Shi, Wang Hui, Shen Sheng-Qiang, Liang Gang-Tao. The drop oscillation model and the comparison with the numerical simulations. Acta Physica Sinica, 2013, 62(20): 204702. doi: 10.7498/aps.62.204702
    [7] Zhao Long, Yang Ji-Ping, Zheng Yan-Hong. Modulation of nonlinear coupling on the synchronization induced by linear coupling. Acta Physica Sinica, 2013, 62(2): 028701. doi: 10.7498/aps.62.028701
    [8] Kuang Yu-Lan, Tang Guo-Ning. Eliminate spiral wave and spatiotemporal chaos by using short-term cardiac memory. Acta Physica Sinica, 2012, 61(19): 190501. doi: 10.7498/aps.61.190501
    [9] Dong Li-Fang, Bai Zhan-Guo, He Ya-Feng. Sparse and dense spiral waves in heterogeneous excitable media. Acta Physica Sinica, 2012, 61(12): 120509. doi: 10.7498/aps.61.120509
    [10] Kuang Yu-Lan, Tang Guo-Ning. Suppressions of spiral waves and spatiotemporal chaos in cardiac tissue. Acta Physica Sinica, 2012, 61(10): 100504. doi: 10.7498/aps.61.100504
    [11] Liu Shao-Bao, Wu Ying, Hao Zhong-Wen, Li Yin-Jun, Jia Ning. Effects of sodium and potassium ion channel fluctuation on the spatiotemporal patterns of neuronal network. Acta Physica Sinica, 2012, 61(2): 020503. doi: 10.7498/aps.61.020503
    [12] Wu Wang-Sheng, Tang Guo-Ning. Synchronizations of chaotic neuronal networks under different couplings. Acta Physica Sinica, 2012, 61(7): 070505. doi: 10.7498/aps.61.070505
    [13] Ma Jun, Xie Zhen-Bo, Chen Jiang-Xing. Numerical study of the death and breakup of spiral wave in the networks of thermosensitive neurons. Acta Physica Sinica, 2012, 61(3): 038701. doi: 10.7498/aps.61.038701
    [14] Wei Hai-Ming, Tang Guo-Ning. Numerical simulation study on effects of alternansbehavior on spiral waves. Acta Physica Sinica, 2011, 60(4): 040504. doi: 10.7498/aps.60.040504
    [15] Wang Jin-Ping, Xu Jian-Ping, Xu Yang-Jun. Analysis of multi-switching period oscillation phenomenon in constant on-time controlled buck converter. Acta Physica Sinica, 2011, 60(5): 058401. doi: 10.7498/aps.60.058401
    [16] Tian Chang-Hai, Deng Min-Yi, Kong Ling-Jiang, Liu Mu-Ren. Cellular automaton simulation with directed small-world networks for the dynamical behaviors of spiral waves. Acta Physica Sinica, 2011, 60(8): 080505. doi: 10.7498/aps.60.080505
    [17] Yang Xian-Qing, Liu Fu, Jia Yan, Deng Min, Guo Hai-Ping, Tang Gang. Oscillations of granular mixture gases with vertical vibration. Acta Physica Sinica, 2010, 59(2): 1116-1122. doi: 10.7498/aps.59.1116
    [18] Gan Zheng-Ning, Ma Jun, Zhang Guo-Yong, Chen Yong. Instability of spiral wave in small-world networks. Acta Physica Sinica, 2008, 57(9): 5400-5406. doi: 10.7498/aps.57.5400
    [19] Xie Fang, Zhu Ya-Bo, Zhang Zhao-Hui, Zhang Lin. Molecular dynamics simulation of multi-wall carbon nanotube oscillators. Acta Physica Sinica, 2008, 57(9): 5833-5837. doi: 10.7498/aps.57.5833
    [20] Ma Jun, Jin Wu-Yin, Li Yan-Long, Chen Yong. Suppression of meandering spiral waves in the excitable media due to a perturbation with stochastic phase. Acta Physica Sinica, 2007, 56(4): 2456-2465. doi: 10.7498/aps.56.2456
  • 期刊类型引用(3)

    1. 赵松,刘丹,罗小元,袁毅. 经颅磁声刺激下分数阶扩展Hindmarsh-Rose神经元放电特性分析. 电子与信息学报. 2022(02): 534-542 . 百度学术
    2. 汪芃,李倩昀,黄志精,唐国宁. 在兴奋-抑制混沌神经元网络中有序波的自发形成. 物理学报. 2018(17): 65-72 . 百度学术
    3. 倪之玮,李新政,白占国,李燕. 反应扩散系统中反螺旋波与反靶波的数值研究. 物理学报. 2018(18): 316-325 . 百度学术

    其他类型引用(2)

Metrics
  • Abstract views:  7911
  • PDF Downloads:  171
  • Cited By: 5
Publishing process
  • Received Date:  27 September 2017
  • Accepted Date:  30 October 2017
  • Published Online:  05 February 2018

/

返回文章
返回