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In this paper, we discuss the effects of heterogeneous neuron arrangement on the frequency synchronization of a ring-coupled FitzHugh-Nagumo neuronal network. The obtained numerical results reveal that the threshold of coupling strength for frequency synchronization may be different for different arrangements of the heterogeneous neurons on a ring. On average, the closer to each other the neurons which are less heterogeneous on a ring, the larger the critical coupling strength needed for neuronal network to achieve frequency synchronization is; the closer to each other the neurons which are more heterogeneous, the smaller the critical coupling strength needed for neuronal network to achieve frequency synchronization is. Furthermore, we give the underlined mechanism for this phenomenon by analyzing the process of frequency synchronization.
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Keywords:
- frequency synchronization /
- heterogeneous neurons /
- neuronal network /
- ring couple
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[1] Uhlhaas P J, Singer W 2006 Neuron 52 155
[2] Shi X, Lu Q S 2004 Chin. Phys. Lett. 21 1695
[3] Wang H X, Lu Q S, Wang Q Y 2005 Chin. Phys. Lett. 22 2173
[4] Neiman A, Schimansky-Geier L, Cornell-Bell A, Moss F 1999 Phys. Rev. Lett. 83 4896
[5] Zhou C S, Kurths J 2003 Chaos 13 401
[6] Shi X, Lu Q S 2005 Chin. Phys. 14 1088
[7] Dhamala M, Jirsa V K, Ding M Z 2004 Phys. Rev. Lett. 92 074104
[8] Wang Q Y, Duan Z S, Perc M, Chen G R 2008 Europhys. Lett. 83 50008
[9] Perc M 2007 Chaos, Solition. Fract. 31 280
[10] Zhou C S, Kurths J, Hu B B 2001 Phys. Rev. Lett. 87 098101
[11] Li Y Y, Jia B, Gu H G, An S C 2012 Commun. Theoret. Phys. 57 817
[12] Wiercigroch M, Ji Q B, Han F, Lu Q S 2009 Chin. Phys. B 18 482
[13] Jia B, Gu H G 2012 Acta Phys. Sin. 61 240505(in Chinese)[贾冰, 古华光 2012 物理学报 61 240505]
[14] Wu Y, Xiao J H, Hu G, Zhan M 2012 Europhys. Lett. 97 40005
[15] Tiitinen H, Sinkkonen J, Reinikainen K, Alho K, Lavikainen J, Nätänen R 1993 Nature 364 59
[16] Pfurtscheller G, Neuper C, Andrew C, Edlinger G 1997 Int. J. Psychophys. 26 121
[17] Fitzhugh R 1961 Biophys. J. 1 445
[18] Nagumo J S, Arimoto S, Yashizawa S 1962 Proc. the IRE 50 2061
[19] Arenas A, Diaz-Guilera A, Kurths J, Moreno Y, Zhou C S 2008 Phys. Reports 469 93
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