相位噪声诱发神经放电的单次或两次相干共振

丁学利; 李玉叶

doi:10.7498/aps.63.248701

摘要

神经元电活动可以从静息通过Hopf分岔到放电, 放电频率有固定周期; 也可以从静息通过鞍-结分岔到放电, 放电频率接近零. 在具有周期性的相位噪声作用下的Hopf分岔和鞍-结分岔点附近, 都会产生相干共振. 噪声的周期小于Hopf分岔点附近的放电的周期时, 相位噪声可以引起神经系统产生一次相干共振, 位于系统内在的固有频率附近; 噪声的周期大于系统的固有周期时, 相位噪声可以引起双共振, 对应低噪声强度的共振产生在噪声频率附近, 对应高噪声强度的共振产生在系统的固有频率附近; 并对双共振的产生原因进行了解释. 在鞍-结分岔点附近, 无论噪声的周期是大是小, 都只会引起一次共振, 研究结果不仅揭示了相位噪声作用下平衡点分岔点相干共振的动力学特性和对应于两类分岔的两类神经兴奋性的差别, 还对近期的相位噪声诱发产生单或双共振的不同研究结果给出了解释.

关键词:

Abstract

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.

Keywords:

作者及机构信息

丁学利¹,
李玉叶²

1.
阜阳职业技术学院基础教学部, 阜阳 236031;

2.
赤峰学院数学与统计学院, 赤峰 024000

基金项目: 内蒙古自然科学基金面上项目(批准号: 2012MS0103)资助的课题.

Authors and contacts

Ding Xue-Li¹,
Li Yu-Ye²

1.
Foundation Department, Fuyang Vocational and Technical College, Fuyang 236031, China;

2.
Mathematics and Statistics institute, Chifeng University, Chifeng 024000, China

Funds: Project supported by Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2012MS0103).

参考文献

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[10]	Zhou C S, Kurths J 2002 Phys. Rev. E 65 040101
[11]	Izhikevich E M 2000 Int. J. Bifurcat. Chaos 10 1171
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[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
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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
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[23]	Zeng L Z, Xu B H 2010 Physica A 22 5128
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[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 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

施引文献

[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 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 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 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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