The stable manifold of the standing wave of the Nagumo equation
The stable manifold of the standing wave of the Nagumo equation
复制标题
Nagumo方程驻波的稳定流形
DOI：
10.1016/0022-0396(89)90086-7
复制
发表时间：
1989
影响因子：
2.4
通讯作者：
G. Flores
中科院分区：
文献类型：
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作者：
G. Flores
沿着神经轴突的电脉冲传导是由霍奇金和赫胥黎描述的。从生理学的角度来看，除了当神经受到低于某一阈值的刺激时，信号被衰减，不传递任何信息外，电压沿神经传播的形状和振幅几乎没有畸变，并且速度几乎是恒定的。数学问题是对行波和稳态进行分类，并证明具有适当初始尺寸和形状的解收敛于其中一个特解。霍奇金和赫胥黎提出的方程的难度导致引入了更简单的神经传导模型。第一个简化是由FitzHugh提出的，他在一类Van der Pol振子中找到了一个很好的模型。根据这一想法，Nagumo等人[111]使用电路来模拟神经轴突。脉冲在这个电路中的传播是由方程组控制的
The conduction of electrical impulses along a nerve axon was described by Hodgkin and Huxley [8]. On physiological grounds, it is expected that the voltage travels along the nerve with little distortion of the shape and amplitude, and at nearly constant speed, except when the nerve is stimulated below a certain threshold, in which case the signal is damped out and no information is transmitted. The mathematical problem is to classify the traveling waves and steady states, and to prove that solutions of appropriate initial size and shape converge to one of these special solutions. The difficulty of the equations proposed by Hodgkin and Huxley has led to the introduction of simpler models of nerve conduction. The first simplification was suggested by FitzHugh [6], who found a good model in a class of Van der Pol oscillators. Following this idea, Nagumo et al.[111 used an electric circuit to simulate a nerve axon. The propagation of pulses in this circuit is governed by the system of equations