Bifurcation and resonance in a model for bursting nerve cells
Bifurcation and resonance in a model for bursting nerve cells
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神经细胞破裂模型中的分叉和共振
DOI：
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发表时间：
1981
影响因子：
1.9
通讯作者：
R. Plant
中科院分区：
文献类型：
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作者：
R. Plant
在本文中，我们考虑一个模型的现象，在神经细胞的爆裂。实验证据表明，这种现象是由于多个电导与非常不同的动力学的相互作用，模型结合了这一证据。作为一个参数的变化，该模型经历了两个振荡波形之间的过渡，实验观察到相应的过渡。在建立了亚临界振荡解的周期性之后，研究了过渡的性质。它被发现是一个共振分岔，在临界点的解分支到另一个相同周期的周期解。使用这个结果之间的比较模型和实验观察。该模型被发现预测，并允许这些意见的解释。
In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.