Analysis of local dynamics of difference and close to them differential-difference equations
type: Item
instance of: scholarly article
title: Analysis of local dynamics of difference and close to them differential-difference equations
zbMATH Open document ID: 1408.34054
DOI: 10.3103/S1066369X18090049
author: I. S. Kashchenko
author: S. A. Kashchenko
published in: Russian Mathematics
publication date: 2019-01-11T00:00:00Z
review text: In this paper, by using the asymptotic expansion techniques and bifurcation theory, the authors study the asymptotic properties of the solutions of the differential-difference equation \[ \gamma\mu^3u'''+\frac12\mu^2u''+\mu u'+u=au(t-1)+f(u(t-1)),\;\;t\in[0,\infty), \] analyzing the cases \(0<\gamma\leq 1/8,\) \(1/8<\gamma<1/2\) and \(\gamma=1/2\) separately and where essentially different results are obtained. Here, \(0<\mu,\varepsilon\ll1\) are small parameters, \(a=-(1+\varepsilon a_1)\) and \(f(u)=f_2u^2+f_3u^3+O(u^4).\)
reviewed by: Robert Vrabel
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34K08
Mathematics Subject Classification ID: 34K27
zbMATH DE Number: 7000197
zbMATH Keywords: bifurcation
zbMATH Keywords: stability
zbMATH Keywords: normal form
zbMATH Keywords: singular perturbation
zbMATH Keywords: dynamics
MaRDI profile type: Publication
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full work available at URL: s1066369x18090049
OpenAlex ID: W2890231495
description: scientific article; zbMATH DE number 7000197