On the connected stability of the large-scale systems of dynamical equations on the time scale in critical cases
type: Item
instance of: scholarly article
title: On the connected stability of the large-scale systems of dynamical equations on the time scale in critical cases
zbMATH Open document ID: 1278.37023
author: S. V. Babenko
author: V. I. Slyn'ko
published in: Journal of Mathematical Sciences (New York)
publication date: 2012-11-28T00:00:00Z
review text: The authors provide a sufficient condition for the trivial solution of the so-called large-scale system \[ x^\Delta (t) = F(t,x), \quad\quad F(t,0 ) = 0 \] to be connectedly stable. Connected stability means that the trivial solution is asymptotically stable for all modified right hand sides \(F(t,Ex)\) with \(E\) a correlation matrix, that is, it has only entries in \(\{0,1\}\). The main assumption consists of the critical case, i.e., the matrix exponential functions and its inverse for the linearized equation are bounded. The long and technically involved proof of the main theorem is based on Lyapunov's direct method.
reviewed by: Stefan Hilger
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34D30
zbMATH DE Number: 6110722
zbMATH Keywords: connected stability
zbMATH Keywords: time scales
zbMATH Keywords: asymptotic stability
MaRDI profile type: Publication
full work available at URL: s10958-012-0725-3
OpenAlex ID: W2082527380
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DOI: 10.1007/S10958-012-0725-3
description: scientific article; zbMATH DE number 6110722