Stability of nonlinear waves in a ring of neurons with delays
type: Item
instance of: scholarly article
title: Stability of nonlinear waves in a ring of neurons with delays
zbMATH Open document ID: 1132.34048
author: Shangjiang Guo
author: Lihong Huang
published in: Journal of Differential Equations
publication date: 2007-06-04T00:00:00Z
review text: In this article a ring of identical neurons with self-feedback and delays is considered. Based on a former existence result of a bifurcation branch of periodic solutions, the authors obtain formulas about the bifurcation direction and stability of the periodic solutions. In particular, properties of phase-locked oscillatory waves, mirror-reflected and standing waves are discussed. The main tools used in the article are normal form theory and center manifold theory.
reviewed by: Marc Georgi
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 92B20
zbMATH DE Number: 5161135
zbMATH Keywords: ring of neurons
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Lie group
zbMATH Keywords: slowly oscillating periodic solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2007.01.027
OpenAlex ID: W2022601797
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DOI: 10.1016/J.JDE.2007.01.027
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description: scientific article; zbMATH DE number 5161135