Stability analysis of a single neuron model with delay

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Abstract

In this paper we study the asymptotic behavior and numerical approximation of the single neuron model equation ẋ(t)=-dx(t)+af (x(t))+bf(x(t-τ))+I, t≥0 (1), where d> 0 and f(x)=0.5(|x+1|- |x-1|). We obtain new sufficient conditions for global asymptotic stability of constant equilibriums of (1), give several numerical examples to illustrate our results, and formulate conjectures on the asymptotic behavior of the solutions based on our numerical experiments.

Original languageEnglish
Pages (from-to)73-92
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume157
Issue number1
DOIs
Publication statusPublished - Aug 1 2003

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Keywords

  • Delayed cellular neural networks
  • Global asymptotic stability
  • Numerical approximations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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