A MODEL OF NEURONAL BURSTING USING 3 COUPLED 1ST ORDER DIFFERENTIAL-EQUATIONS
A MODEL OF NEURONAL BURSTING USING 3 COUPLED 1ST ORDER DIFFERENTIAL-EQUATIONS
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DOI：
10.1098/rspb.1984.0024
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发表时间：
1984-01-01
期刊：
影响因子：
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通讯作者：
ROSE, RM
中科院分区：
文献类型：
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作者：
HINDMARSH, JL;ROSE, RM
对最近的动作电位模型进行了修正，引入了两个额外的平衡点。通过稳定性分析，证明了这些平衡点中的1个是鞍点，在鞍点上有两个分离线，它们将相平面分成两个区域。在1个区域中，所有相路径都接近极限环，而在另一个区域中，所有相路径都接近稳定平衡点。其结果是，一个短的去极化电流脉冲将改变池塘蜗牛最初沉默的模型神经元，变成一个重复放电的神经元。第三个方程的加入将这种激发限制为孤立的爆发或去极化的后电势。当对该模型施加稳定的去极化电流时，它会导致周期性爆发。这些方程最初是用来解释孤立触发爆发的，因此提供了振荡爆发放电这一更为普遍的现象的最简单模型之一。
A modification to a recent model of the action potential which introduces 2 additional equilibrium points is described. By using stability analysis 1 of these equilibrium points is shown to be a saddle point from which there are 2 separatrices which divide the phase plane into 2 regions. In 1 region all phase paths approach a limit cycle and in the other all phase paths approach a stable equilibrium point. A consequence of this is that a short depolarizing current pulse will change an initially silent model neuron of the pond snail into one that fires repetitively. Addition of a 3rd equation limits this firing to either an isolated burst or a depolarizing afterpotential. When steady depolarizing current was applied to this model it resulted in periodic bursting. The equations, which were initially developed to explain isolated triggered bursts, therefore provide one of the simplest models of the more general phenomenon of oscillatory burst discharge.