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Neuronal firing activity can be changed from the resting state to firing state either through Hopf bifurcation where the firing exhibits a fixed period or through saddle-node bifurcation where the firing frequency is nearly zero. Phase noise with periodicity can induce coherence resonances near Hopf and saddle-node bifurcation points. When the period of phase noise is shorter than the internal period of firing near the Hopf bifurcation point, the phase noise can induce single coherence resonance appearing near the frequency of the phase noise. When the period of phase noise is longer than the internal period of firing near the Hopf bifurcation point, the phase noise can induce double coherence resonances. The resonance at low noise intensity appears near the frequency of the phase noise, and the one at large noise intensity occurs near the frequency of the firing near the Hopf bifurcation. The mechanism of the double resonances is explained. Unlike the Hopf bifurcation point, only a single coherence resonance can be induced near the saddle-node bifurcation point by the phase noise with long or short periods. The results not only reveal the dynamics of phase noise induced coherence resonance of the equilibrium point and identify the distinction between two types of neuronal excitabilities corresponding to two kinds of bifurcations, but also provide an explanation about the different results of phase noise induced single or double resonances simulated in recent studies.
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Keywords:
- coherence resonance /
- phase noise /
- Hopf bifurcation /
- saddle-node bifurcation
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[2] Longtin A, Bulsara A, Moss F 1991 Phys. Rev. Lett. 67 656
[3] Gu H G, Ren W, Lu Q S, Wu S G, Yang M H, Chen W J 2001 Phys. Lett. A 285 63
[4] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2002 Neuro Report 13 1657
[5] Yang M H, Li L, Liu Z Q, Xu Y L, Liu H J, Gu H G, Ren W 2009 Int. J. Bifurcat. Chaos 19 453
[6] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[7] Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365 337
[8] Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130
[9] Hu G, Ditzinger T, Ning C, Haken H 1993 Phys. Rev. Lett. 71 807
[10] Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101
[11] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[12] Hodgkin A 1948 J. Physiol. 107 165
[13] Rinzel J, Ermentrout G B 1989 Analysis of Neural Excitability and Oscillations (Cambridge: The MIT Press) p135
[14] Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011 Int. J. Mod. Phys. B 25 3977
[15] Jia B, Gu H G 2012 Cogn. Neurodyn. 6 485
[16] Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2004 Chin. Phys. 13 1396
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[21] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Int. J. Mod. Phys. B 17 4195
[22] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Phys. Lett. A 319 89
[23] Zeng L Z, Xu B H 2010 Physica A 22 5128
[24] Gu H G, Zhu Z, Jia B 2011 Acta Phys. Sin. 60 100505 (in Chinese) [古华光, 朱洲, 贾冰 2011 物理学报 60 100505]
[25] Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952
[26] Liu W, Zhu W, Huang Z 2001 Chaos Soliton. Fract. 12 527
[27] Demir A, Mehrotra A, Roychowdhury J 2000 IEEE Trans. Circuits Syst. 47 655
[28] Xi L X, Li J P, Du S C, Xu X, Zhao X G 2011 Chin. Phys. B 20 024214
[29] Chen W, Meng Z, Zhou H J, Luo H 2012 Chin. Phys. B 21 034212
[30] Ma Y X, Xi L X, Chen G, Zhang X G 2012 Chin. Phys. B 21 064222
[31] Kang X S, Liang X M, Lu H P 2013 Chin. Phys. Lett. 30 018701
[32] Liang X M, Zhao L, Liu Z H 2011 Phys. Rev. E 84 031916
[33] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[34] Tateno T, Pakdaman K 2004 Chaos 14 511
[35] Tsumoto K, Kitajima H, Yoshinaga T, Aihara K, Kawakami H 2006 Neurocomputing 69 293
[36] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504
[37] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010 Physica A 389 2642
[38] Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 物理学报 61 070504]
[39] Gu H G, Jia B, Lu Q S 2011 Cogn. Neurodyn. 5 87
[40] Xie Y, Xu J X, Hu S J 2004 Chaos Soliton. Fract. 21 177
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[1] Braun H A, Wissing H, Schäfer K, Hirsch M C 1994 Nature 367 270
[2] Longtin A, Bulsara A, Moss F 1991 Phys. Rev. Lett. 67 656
[3] Gu H G, Ren W, Lu Q S, Wu S G, Yang M H, Chen W J 2001 Phys. Lett. A 285 63
[4] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2002 Neuro Report 13 1657
[5] Yang M H, Li L, Liu Z Q, Xu Y L, Liu H J, Gu H G, Ren W 2009 Int. J. Bifurcat. Chaos 19 453
[6] Benzi R, Sutera A, Vulpiani A 1981 J. Phys. A 14 L453
[7] Douglass J K, Wilkens L, Pantazelou E, Moss F 1993 Nature 365 337
[8] Jung P, Mayer-Kress G 1995 Phys. Rev. Lett. 74 2130
[9] Hu G, Ditzinger T, Ning C, Haken H 1993 Phys. Rev. Lett. 71 807
[10] Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101
[11] Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
[12] Hodgkin A 1948 J. Physiol. 107 165
[13] Rinzel J, Ermentrout G B 1989 Analysis of Neural Excitability and Oscillations (Cambridge: The MIT Press) p135
[14] Gu H G, Zhang H M, Wei C L, Yang M H, Liu Z Q, Ren W 2011 Int. J. Mod. Phys. B 25 3977
[15] Jia B, Gu H G 2012 Cogn. Neurodyn. 6 485
[16] Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2004 Chin. Phys. 13 1396
[17] Tateno T, Harsch A, Robinson H 2004 J. Neurophysiol. 92 2283
[18] Morris C, Lecar H 1981 Biophys. J. 35 193
[19] FitzHugh R 1961 Biophys. J. 1 445
[20] Gu H G, Xi L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 物理学报 61 080504]
[21] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Int. J. Mod. Phys. B 17 4195
[22] Gu H G, Yang M H, Li L, Liu Z Q, Ren W 2003 Phys. Lett. A 319 89
[23] Zeng L Z, Xu B H 2010 Physica A 22 5128
[24] Gu H G, Zhu Z, Jia B 2011 Acta Phys. Sin. 60 100505 (in Chinese) [古华光, 朱洲, 贾冰 2011 物理学报 60 100505]
[25] Zhang Y, Hu G, Gammaitoni L 1998 Phys. Rev. E 58 2952
[26] Liu W, Zhu W, Huang Z 2001 Chaos Soliton. Fract. 12 527
[27] Demir A, Mehrotra A, Roychowdhury J 2000 IEEE Trans. Circuits Syst. 47 655
[28] Xi L X, Li J P, Du S C, Xu X, Zhao X G 2011 Chin. Phys. B 20 024214
[29] Chen W, Meng Z, Zhou H J, Luo H 2012 Chin. Phys. B 21 034212
[30] Ma Y X, Xi L X, Chen G, Zhang X G 2012 Chin. Phys. B 21 064222
[31] Kang X S, Liang X M, Lu H P 2013 Chin. Phys. Lett. 30 018701
[32] Liang X M, Zhao L, Liu Z H 2011 Phys. Rev. E 84 031916
[33] Hodgkin A L, Huxley A F 1952 J. Physiol. 117 500
[34] Tateno T, Pakdaman K 2004 Chaos 14 511
[35] Tsumoto K, Kitajima H, Yoshinaga T, Aihara K, Kawakami H 2006 Neurocomputing 69 293
[36] Li Y Y, Zhang H M, Wei C L, Yang M H, Gu H G, Ren W 2009 Chin. Phys. Lett. 26 030504
[37] Liu Z Q, Zhang H M, Li Y Y, Hua C C, Gu H G, Ren W 2010 Physica A 389 2642
[38] Li Y Y, Jia B, Gu H G 2012 Acta Phys. Sin. 61 070504 (in Chinese) [李玉叶, 贾冰, 古华光 2012 物理学报 61 070504]
[39] Gu H G, Jia B, Lu Q S 2011 Cogn. Neurodyn. 5 87
[40] Xie Y, Xu J X, Hu S J 2004 Chaos Soliton. Fract. 21 177
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