Asymptotic behavior of Morris-Lecar system
type: Item
instance of: scholarly article
title: Asymptotic behavior of Morris-Lecar system
zbMATH Open document ID: 1160.34330
author: Jiang Wang
author: Meili Lu
author: Xiangyang Fei
author: Xiao-Wei Ye
published in: Nonlinear Analysis. Real World Applications
publication date: 2008-07-21T00:00:00Z
review text: The Morris-Lecar system describes the behavior of a neuron based on the flow of potassium and calcium ions. It is a system of two autonomous ordinary differential equations of the type \[ {dx\over dt}= f(x,y,\alpha),\quad {dy\over dt}= g(x,y,\alpha),\tag{\(*\)} \] where \(\alpha\) is some parameter vector. For certain parameter vector \(\alpha_0\), the authors embed \((*)\) into the family of singularly perturbed systems \[ \varepsilon{dx\over dt}= f(x,y,\alpha_0),\quad {dy\over dt}= g(x,y,\alpha) \] and claim that Tichonov's theory can be applied to explain the spiking behavior of \((*)\).
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 92C20
Mathematics Subject Classification ID: 34E05
zbMATH DE Number: 5303253
zbMATH Keywords: Morris-Lecar system
zbMATH Keywords: fast-slow system
zbMATH Keywords: asymptotic structure
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2007.01.005
OpenAlex ID: W2034573118
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DOI: 10.1016/J.NONRWA.2007.01.005
description: scientific article; zbMATH DE number 5303253