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2006•International Journal of Bifurcation and ChaosRequires access

MULTIPLE BIFURCATION ANALYSIS IN A NEURAL NETWORK MODEL WITH DELAYS

Yuan Yuan, Junjie Wei

Open publisher page 20 citations

Abstract

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.

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What this paper is about

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.

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Available abstract

A synchronized neural network model with delays is considered. The bifurcations arising from the zero root of the corresponding characteristic equation have been studied by employing the center manifold theorem, normal form method and bifurcation theory. It is shown that the system may exhibit transcritical/pitchfork bifurcation, or Bogdanov–Takens bifurcation. Some numerical simulation examples are given to justify the theoretical results.

Key concepts: Pitchfork bifurcation, Center manifold, Transcritical bifurcation, Bogdanov–Takens bifurcation, Biological applications of bifurcation theory, Saddle-node bifurcation, Mathematics, Bifurcation diagram

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