Qualitative analysis of a neural network model with multiple time delays

Sue Ann Campbell, Shigui Ruan, Junjie Wei

Research output: Contribution to journalArticle

68 Citations (Scopus)

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
StatePublished - Aug 1999
Externally publishedYes

Fingerprint

Multiple Time Delays
Qualitative Analysis
Neural Network Model
Neurons
Neuron
Time delay
Neural networks
Transcendental function
Hopf bifurcation
Characteristic equation
Transcendental
Local Stability
Linear Stability
Hopf Bifurcation
Stability Analysis
Scalar
Ring
Sufficient Conditions

ASJC Scopus subject areas

  • General
  • Applied Mathematics

Cite this

Qualitative analysis of a neural network model with multiple time delays. / Campbell, Sue Ann; Ruan, Shigui; Wei, Junjie.

In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 9, No. 8, 08.1999, p. 1585-1595.

Research output: Contribution to journalArticle

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