Qualitative analysis of a neural network model with multiple time delays

Sue Ann Campbell, Shigui Ruan, Junjie Wei

Research output: Contribution to journalArticle

70 Scopus citations

Abstract

We consider a simplified neural network model for a ring of four neurons where each neuron receives two time delayed inputs: One from itself and another from the previous neuron. Local stability analysis of the positive equilibrium leads to a characteristic equation containing products of four transcendental functions. By analyzing the equivalent system of four scalar transcendental equations, we obtain sufficient conditions for the linear stability of the positive equilibrium. Furthermore, we show that a Hopf bifurcation can occur when the positive equilibrium loses stability.

Original languageEnglish (US)
Pages (from-to)1585-1595
Number of pages11
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume9
Issue number8
DOIs
StatePublished - Aug 1999

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ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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