Integral manifolds, stability, and bifurcation of solutions of singularly perturbed functional-differential equations
type: Item
instance of: scholarly article
title: Integral manifolds, stability, and bifurcation of solutions of singularly perturbed functional-differential equations
zbMATH Open document ID: 0617.34037
DOI: 10.1007/BF01056826
author: V. I. Fodchuk
author: I. I. Klevchuk
author: Yu. A. Mitropol'skij
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The integral manifolds and stability zero solution of the system \[ \dot x(t)=F(t,x(t),y_ t),\quad \epsilon \dot y(t)=G_ 1(t,x(t),y_ t), \] where \(x(t)\in {\mathbb{R}}^ m\), \(y(t)\in {\mathbb{R}}^{\ell}\), \(y_ t(\theta)=y(t+\theta)\), -\(\epsilon\Delta\leq \theta \leq 0\) are investigated. The bifurcation of the solution of the system \[ \dot x(t)=\xi x(t)+\eta y(t)\to \zeta y(t-\epsilon \Delta)+F(x(t),y(t),y(t- \epsilon \Delta)) \] \[ \epsilon \dot y(t)=By(t)+Cy(t-\epsilon \Delta)+Dx(t)+G(x(t),y(t),y(t-\epsilon \Delta)) \] is also studied.
Mathematics Subject Classification ID: 34C30
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 4000433
zbMATH Keywords: integral manifolds
zbMATH Keywords: bifurcation
MaRDI profile type: Publication
cites work: Q5551699
cites work: Integral sets and the reduction principle for differential-functional equations
description: scientific article; zbMATH DE number 4000433