中国物理B ›› 2004, Vol. 13 ›› Issue (9): 1396-1401.doi: 10.1088/1009-1963/13/9/005

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Characteristics of critical amplitude of a sinusoidal stimulus in a model neuron

段玉斌1, 胡三觉2, 谢勇3, 徐健学3, 康艳梅3   

  1. (1)Department of Physiology, The Fourth Military University, Xi'an 710032, China; (2)Institute of Neuroscience, The Fourth Military University, Xi'an 710032, China; (3)State Key Laboratory of Mechanical Structural Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2003-07-24 修回日期:2003-12-19 出版日期:2004-06-21 发布日期:2005-06-21
  • 基金资助:
    Project supported by the National Key Natural Science Foundation of China (Grant No 30030040).

Characteristics of critical amplitude of a sinusoidal stimulus in a model neuron

Xie Yong (谢勇)a, Xu Jian-Xue (徐健学)a, Kang Yan-Mei (康艳梅)a, Hu San-Jue (胡三觉)b, Duan Yu-Bin (段玉斌)c    

  1. a State Key Laboratory of Mechanical Structural Strength and Vibration, Xi'an Jiaotong University, Xi'an 710049, China; b Institute of Neuroscience, The Fourth Military University, Xi'an 710032, China; c Department of Physiology, The Fourth Military University, Xi'an 710032, China
  • Received:2003-07-24 Revised:2003-12-19 Online:2004-06-21 Published:2005-06-21
  • Supported by:
    Project supported by the National Key Natural Science Foundation of China (Grant No 30030040).

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摘要： The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.

关键词: stochastic resonance, Hopf bifurcation, saddle-node on invariant circle bifurcation, Morris－Lecar model

Abstract: The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.

Key words: stochastic resonance, Hopf bifurcation, saddle-node on invariant circle bifurcation, Morris－Lecar model

中图分类号:  (General theory and mathematical aspects)

  • 87.10.-e
87.18.Sn (Neural networks and synaptic communication) 05.45.-a (Nonlinear dynamics and chaos) 05.10.Gg (Stochastic analysis methods)