Stability and bifurcation in a neural network model with two delays

Junjie Wei, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

329 Scopus citations

Abstract

A simple neural network model with two delays is considered. Linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. For the case without self-connection, it is found that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulations are performed to illustrate the obtained results.

Original languageEnglish (US)
Pages (from-to)255-272
Number of pages18
JournalPhysica D: Nonlinear Phenomena
Volume130
Issue number3-4
DOIs
StatePublished - Jun 15 1999
Externally publishedYes

Keywords

  • Hopf bifurcation
  • Neural networks
  • Periodic solutions
  • Stability
  • Time delay

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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