Traveling waves and pulses in a one-dimensional network of excitable integrate-and-5re neurons
Traveling waves and pulses in a one-dimensional network of excitable integrate-and-5re neurons
复制标题
可兴奋整合和 5re 神经元的一维网络中的行波和脉冲
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
P. C. Bresslo
中科院分区：
文献类型：
--
作者：
P. C. Bresslo
本文研究了具有突触耦合的一维整合-再整合神经元网络中行波和脉冲的存在性和稳定性。这提供了一个简单的可兴奋神经组织模型。我们首先导出了行波存在的自洽条件，它产生了速度和波长之间的色散关系。我们用它来研究波传播如何依赖于表征神经元相互作用的各种参数，如突触和轴突延迟，以及树突电缆的被动膜特性。我们还建立了可激发网络支持孤立脉冲在长波长限制的传播。然后，我们利用线性化的“环时间映象”的特征方程，导出了行波（局部）渐近稳定的一般条件。nite顺序的存在方程。我们用它来分析孤立脉冲在长波长极限下的稳定性。孤波的解决方案是成对的更快（更慢）的解决方案稳定（不稳定）的情况下，零轴突延迟;非零延迟和快速突触的稳定波本身可以通过一个Hopf分叉不稳定。
We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-"re neuronswith synaptic coupling. This provides a simple model of excitable neural tissue. We "rst derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation dependson variousparametersthat characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane proper- ties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling wavesin termsof the characteris tic equation of the lin- earized "ring time map, which takesthe form of an integro-di !erence equation of in"nite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation.
影响因子：
2.5
作者：
CHERVIN, RD;PIERCE, PA;CONNORS, BW
通讯作者：
CONNORS, BW