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首页> 外文期刊>Journal of Computational Neuroscience >The Onset and Extinction of Neural Spiking: A Numerical Bifurcation Approach
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The Onset and Extinction of Neural Spiking: A Numerical Bifurcation Approach

机译:神经突增的发作和消退:一种数值分叉方法

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We study the onset of neural spiking when the equilibrium rest state loses stability by the change of a critical parameter, the applied current. In the case of the well-known Morris-Lecar model, we start from a complete numerical study of the bifurcation diagram in the most relevant two-parameter range. This diagram includes all equilibrium and limit cycle bifurcations, thus correcting and completing earlier studies. We discuss and classify the behavior of the spiking orbits, when increasing or decreasing the applied current. A complete classification can be extracted from the complete bifurcation diagram. It is based on three components: bifurcation type of the equilibrium at the loss of stability, subcritical behavior in the limit of decreasing the applied current and supercritical behavior in the limit of increasing the applied current.
机译:当平衡静止状态由于临界参数(施加电流)的变化而失去稳定性时,我们研究了神经尖峰的发作。对于著名的Morris-Lecar模型,我们从最相关的两参数范围内的分叉图的完整数值研究开始。该图包括所有平衡和极限循环分支,从而纠正并完成了较早的研究。当增加或减小施加的电流时,我们讨论并分类了尖峰轨道的行为。可以从完整的分叉图中提取完整的分类。它基于以下三个组成部分:稳定性损失的平衡的分叉类型,在减小施加电流的极限范围内的亚临界行为和在增加施加电流的极限范围内的超临界行为。

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