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

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dc.creatorBraverman, Elena
dc.creatorZhukovskiy, Sergey
dc.date2009-01-09
dc.date.accessioned2026-07-07T12:28:05Z
dc.date.available2026-07-07T12:28:05Z
dc.descriptionWe 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.
dc.description23 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0901.1283
dc.identifierhttp://arxiv.org/abs/0901.1283
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215425
dc.subjectDynamical Systems
dc.subject34K20; 92D25; 34K60; 34K23
dc.titleAbsolute and Delay-Dependent Stability of Equations with a Distributed Delay: a Bridge from Nonlinear Differential to Difference Equations
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