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Response characteristics of FitzHugh-Nagumo neurons to low frequency signal have been investigated by numerical simulation. Neurons are arranged on a square-lattice and are subjected to two frequency signals. Results show that, vibrational resonance of the membrane potential can be induced by varying the amplitude of the high-frequency signal, when the control parameter is selected in the excitable region. In addition, the responses of neurons to higher harmonics of low-frequency signal have been studied, and nonlinear vibrational resonances are also found. With the increase of frequency in the low-frequency signal, the response of the system to low-frequency signal can resonate. Thus, the double resonance can occur by changing the frequency in low-frequency signal and the amplitude in high-frequency signal. Moreover, effects of electrical synapses and chemical synapses on vibrational resonance and nonlinear vibrational resonance of the neurons have also been studied. Effect of the number of neurons, which are subjected to two frequency signals in the square-lattice, on the response characteristic of the system is also studied. It is found that the response characteristic of the electrical coupling neurons is quite different from that of chemical coupling neurons.
[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2] Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[3] Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Wang M S 2009 Acta Phys. Sin. 57 4667 (in Chinese) [汪茂胜 2009 物理学报 57 4667]
[5] Wang B, Sun Y Q, Tang X D 2013 Chin. Phys. B 22 010501
[6] Guo F, Cheng X F, Li S F, Cao W, Li H 2012 Chin. Phys. B 21 080502
[7] Fauve S, Hesot F 1983 Phys. Lett. A 97 5
[8] Marino F, Giudici M, Barland S 2002 Phys. Rev. Lett. 88 040601
[9] Pikovsky A, Kurths J 1997 Phys. Rev. Lett. 78 775
[10] Jiang Y, Zhong S, Xin H 2000 J. Phys. Chem. A 104 8521
[11] Chizhevsky V N, Giovanni G 2006 Phys. Rev. E. 73 022103
[12] Chizhevsky V N, Giovanni G 2008 Phys. Rev. E 77 051126
[13] Yu H T, Wang J 2013 Acta Phys. Sin. 62 170511 (in Chinese) [于海涛, 王江 2013 物理学报 62 170511]
[14] Ullner E, Zaikin A, García-Ojalvo J, Báscones R, Kurths J 2003 Physics Letters A 312 348
[15] Hodgkin A L, Huxley A F 1952 J. Physiol. 116 473
[16] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[17] FitzHugh R 1961 Biophys. J. 1 445
[18] Morris C, Lecar H 1981 Biophys. J. 35 193
[19] Hindmash L J, Rose M R 1984 Proc. R. Soc. Lond. B 221 87
[20] WangM S, HouZ H, Xing, H W 2006 Chin. Phys. Lett. 23 2666
[21] Deng B, Wang J, Wei X L 2009 Chaos 19 013117
[22] Men C, Wang J, Qin Y M, Deng B, Tsang K M, Chan W L 2012 Chaos 22 013104
[23] Gammaitoni L, Hänggi P, Jung P, Marachesoni F 1998 Rev. Mod. Phys. 70 223
[24] Zaikin A A, García-Ojalvo J, Schimansky-Geier L, Kurths J 2001 Phys. Rev. Lett. 88 010601
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[1] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[2] Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[3] Gammaitoni L, Hänggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[4] Wang M S 2009 Acta Phys. Sin. 57 4667 (in Chinese) [汪茂胜 2009 物理学报 57 4667]
[5] Wang B, Sun Y Q, Tang X D 2013 Chin. Phys. B 22 010501
[6] Guo F, Cheng X F, Li S F, Cao W, Li H 2012 Chin. Phys. B 21 080502
[7] Fauve S, Hesot F 1983 Phys. Lett. A 97 5
[8] Marino F, Giudici M, Barland S 2002 Phys. Rev. Lett. 88 040601
[9] Pikovsky A, Kurths J 1997 Phys. Rev. Lett. 78 775
[10] Jiang Y, Zhong S, Xin H 2000 J. Phys. Chem. A 104 8521
[11] Chizhevsky V N, Giovanni G 2006 Phys. Rev. E. 73 022103
[12] Chizhevsky V N, Giovanni G 2008 Phys. Rev. E 77 051126
[13] Yu H T, Wang J 2013 Acta Phys. Sin. 62 170511 (in Chinese) [于海涛, 王江 2013 物理学报 62 170511]
[14] Ullner E, Zaikin A, García-Ojalvo J, Báscones R, Kurths J 2003 Physics Letters A 312 348
[15] Hodgkin A L, Huxley A F 1952 J. Physiol. 116 473
[16] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[17] FitzHugh R 1961 Biophys. J. 1 445
[18] Morris C, Lecar H 1981 Biophys. J. 35 193
[19] Hindmash L J, Rose M R 1984 Proc. R. Soc. Lond. B 221 87
[20] WangM S, HouZ H, Xing, H W 2006 Chin. Phys. Lett. 23 2666
[21] Deng B, Wang J, Wei X L 2009 Chaos 19 013117
[22] Men C, Wang J, Qin Y M, Deng B, Tsang K M, Chan W L 2012 Chaos 22 013104
[23] Gammaitoni L, Hänggi P, Jung P, Marachesoni F 1998 Rev. Mod. Phys. 70 223
[24] Zaikin A A, García-Ojalvo J, Schimansky-Geier L, Kurths J 2001 Phys. Rev. Lett. 88 010601
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