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The synchronization of a two-dimensional (2D) neuronal network is investigated, based on the dynamical model of Hindmarsh-Rose neuron. In order to know the effects of different types of coupling on the synchronization of a network, we propose three coupling schemes. They are the general feedback coupling, the hierarchical feedback couplings with and without local mean field. The numerical results show that when the neighbor coupling strength is small, the hierarchical feedback couplings with and without local mean field can achieve local and global synchronizations of the network, whereas the general feedback coupling cannot achieve global synchronization. Different couplings generate different patterns in the corresponding network, so that the processes of the transition from asynchronization to synchronization in the networks are different. With the increase of coupling strength, the synchronization in the network with the general feedback or hierarchical feedback couplings is suddenly established, and the networks exhibit different coherent patterns that are aperiodic before the global synchronization occurs. However, the network with hierarchical feedback couplings and local mean field exhibits the different synchronous processes. The neurons in the same layer first achieve the transition from bursting synchronization to global synchronization, leading to the formation of target wave. Then, the synchronization region gradually expands from the center of the network. Finally, the whole networks can achieve synchronization. These results show that the lossless signal transmission can be achieved only if the appropriate coupling is applied. In addition, we find that the hierarchical feedback coupling with local mean field can facilitate synchronization.
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Keywords:
- Hindmarsh-Rose neural /
- local mean field /
- synchronization
[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Baptista M S, Moukam Kakmeni F M, Grebogi C 2010 Phys. Rev.E 82 036203
[3] Rappel W J, Karma A 1996 Phys. Rev. Lett. 77 3256
[4] Dhamala M, Jirsa V K, DingMZ 2004 Phys. Rev. Lett. 92 074104
[5] Rosenblum M G, Pikovsky A S 2004 Phys. Rev. Lett. 92 114102
[6] Yu H J, Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese)[于洪吉, 童伟君 2009 58 2977]
[7] Zhou J, Liu Z H 2008 Phys. Rev. E 77 056213
[8] Tang Y, Qiu R, Fang J A, Miao Q Y 2008 Phys. Lett. A 372 4425
[9] Wang H X, Lu Q S, Wang Q Y 2005 Chin. Phys. Lett. 22 2173
[10] He G G, Zhu P, Chen H P, Xie X P 2010 Acta Phys. Sin. 595307(in Chinese)[何国光, 朱萍, 陈宏平, 谢小平 2010 59 5307]
[11] Shahverdiev E M, Shore K A 2005 Phys. Rev. E 71 016201
[12] Wang H X, Lu Q S, Shi X 2010 Chin. Phys. B 19 060509
[13] Zeitler M, Daffertshofer A, Gielen C C A M 2009 Phys. Rev. E79 065203
[14] Englert A, Kinzel W, Aviad Y, Butkovski M, Reidler I, Zigzag M,Kanter I, Rosenbluh M 2010 Phys. Rev. Lett. 104 114102
[15] Ma J, Su WT, Gao J Z 2010 Acta Phys. Sin. 59 1554 (in Chinese)[马军, 苏文涛, 高加振 2010 59 1554]
[16] Yu J, Hu C, Jiang H J, Teng Z D 2011 Neurocomputing 74 1776
[17] Wang Q Y, Chen G R, Perc M 2011 PLoS ONE 6 e15851
[18] Shi X, Lu Q S 2007 Chin. Phys. Lett. 24 636
[19] Sheeba J H, Chandrasekar V K, Lakshmanan M 2009 Phys. Rev.E 79 055203
[20] Huerta R, Bhazenov M, Rabinovich M I 1998 Europhys. Lett. 43719
[21] Mainieri M S, Erichsen Jr R, Brunnet L G 2005 Physica A 354663
[22] Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87
[23] Lu Q S, Liu S Q, Liu F, Wang Q Y, Hou Z H, Zheng Y H 2008Adv. Mech. 38 766 (in Chinese)[陆启韶, 刘深泉, 刘峰, 王青云, 候中怀, 郑艳红 2008 力学进展 38 766]
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[1] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2] Baptista M S, Moukam Kakmeni F M, Grebogi C 2010 Phys. Rev.E 82 036203
[3] Rappel W J, Karma A 1996 Phys. Rev. Lett. 77 3256
[4] Dhamala M, Jirsa V K, DingMZ 2004 Phys. Rev. Lett. 92 074104
[5] Rosenblum M G, Pikovsky A S 2004 Phys. Rev. Lett. 92 114102
[6] Yu H J, Tong W J 2009 Acta Phys. Sin. 58 2977 (in Chinese)[于洪吉, 童伟君 2009 58 2977]
[7] Zhou J, Liu Z H 2008 Phys. Rev. E 77 056213
[8] Tang Y, Qiu R, Fang J A, Miao Q Y 2008 Phys. Lett. A 372 4425
[9] Wang H X, Lu Q S, Wang Q Y 2005 Chin. Phys. Lett. 22 2173
[10] He G G, Zhu P, Chen H P, Xie X P 2010 Acta Phys. Sin. 595307(in Chinese)[何国光, 朱萍, 陈宏平, 谢小平 2010 59 5307]
[11] Shahverdiev E M, Shore K A 2005 Phys. Rev. E 71 016201
[12] Wang H X, Lu Q S, Shi X 2010 Chin. Phys. B 19 060509
[13] Zeitler M, Daffertshofer A, Gielen C C A M 2009 Phys. Rev. E79 065203
[14] Englert A, Kinzel W, Aviad Y, Butkovski M, Reidler I, Zigzag M,Kanter I, Rosenbluh M 2010 Phys. Rev. Lett. 104 114102
[15] Ma J, Su WT, Gao J Z 2010 Acta Phys. Sin. 59 1554 (in Chinese)[马军, 苏文涛, 高加振 2010 59 1554]
[16] Yu J, Hu C, Jiang H J, Teng Z D 2011 Neurocomputing 74 1776
[17] Wang Q Y, Chen G R, Perc M 2011 PLoS ONE 6 e15851
[18] Shi X, Lu Q S 2007 Chin. Phys. Lett. 24 636
[19] Sheeba J H, Chandrasekar V K, Lakshmanan M 2009 Phys. Rev.E 79 055203
[20] Huerta R, Bhazenov M, Rabinovich M I 1998 Europhys. Lett. 43719
[21] Mainieri M S, Erichsen Jr R, Brunnet L G 2005 Physica A 354663
[22] Hindmarsh J L, Rose R M 1984 Proc. R. Soc. Lond. B 221 87
[23] Lu Q S, Liu S Q, Liu F, Wang Q Y, Hou Z H, Zheng Y H 2008Adv. Mech. 38 766 (in Chinese)[陆启韶, 刘深泉, 刘峰, 王青云, 候中怀, 郑艳红 2008 力学进展 38 766]
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