Absolute and Delay-Dependent Stability of Equations with a Distributed Delay: a Bridge from Nonlinear Differential to Difference Equations

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant difference equation such that its stability implies stability of the equation with a distributed delay and a finite memory. This result is, generally speaking, incorrect for systems with infinite memory. If the relevant difference equation is unstable, we describe the general delay-independent attracting set and also demonstrate that the equation with a distributed delay is stable for small enough delays.
23 pages, 4 figures

Keywords

Dynamical Systems, 34K20; 92D25; 34K60; 34K23

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/215425

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0901.1283
 http://arxiv.org/abs/0901.1283

Collections

arXiv