Global stability in delay differential systems without dominating instantaneous negative feedbacks
type: Item
instance of: scholarly article
title: Global stability in delay differential systems without dominating instantaneous negative feedbacks
zbMATH Open document ID: 0828.34066
author: Yang Kuang
published in: Journal of Differential Equations
publication date: 1996-01-02T00:00:00Z
review text: The systems \(x_i'(t)= x_i(t) f_i(t, x_t(\cdot))\), \(i= 1,\dots, n\) and \(x_i'(t)= x_i(t) f_i(t, x_t(\cdot), y_t(\cdot))\), \(i= 1,\dots, n\), \(y_j'(t)= g_j(t, x_t(\cdot), y_t(\cdot))\), \(j= 1,\dots, m\) are considered with \(f_i\) and \(g_j\) continuous linear operators. It is shown that if the systems have globally asymptotically stable nonnegative equilibria in the absence of the delays and if the systems are dissipative if delays are present (solutions are eventually uniformly bounded), then the equilibria remain globally asymptotically stable as long as the time lags involved in some part of the negative feedbacks are small enough.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 784950
zbMATH Keywords: delayed Lotka-Volterra systems
zbMATH Keywords: global stability
zbMATH Keywords: negative feedbacks
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1100
OpenAlex ID: W2092740910
DOI: 10.1006/JDEQ.1995.1100
description: scientific article; zbMATH DE number 784950