On the global attractivity of non-autonomous neural networks with a distributed delay

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider a system of s nonlinear differential equations with a distributed delay dxi dt = gi(t)[ ∫t hi1(t) dτ1 ri1(t, τ1) . . . ∫t his(t) fi(x1(τ1), x2(τ2), . . . , xs(τs))dτs ris(t, τs) - xi(t)] and obtain global asymptotic stability conditions, which are independent of delays. The ideas of the proofs are based on the notion of a strong attractor of a vector difference equation associated with a nonlinear vector differential equation. The results are applied to Hopfield neural networks and to compartment-type models of population dynamics with Nicholson's blowflies growth law.

Original languageEnglish
Pages (from-to)2381-2401
Number of pages21
JournalNonlinearity
Volume34
Issue number4
DOIs
StatePublished - 1 Apr 2021

Keywords

  • Distributed delay
  • Global attractivity
  • Neural networks
  • Nicholson's blowflies model
  • Non-autonomous systems of differential equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)
  • Applied Mathematics

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