Stability, bifurcation analysis in a neural network model with delay and diffusion

Rui Hu; Yuan Yuan

doi:10.3934/proc.2009.2009.367

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2009, Volume 2009: 367-376. Doi: 10.3934/proc.2009.2009.367 open access

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Stability, bifurcation analysis in a neural network model with delay and diffusion

Rui Hu^1, and
Yuan Yuan^1,

1.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, Canada A1C 5S7

Received: June 30, 2008

Revised: June 30, 2009

Published: June 2009

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Abstract

We consider a delayed neural network model with diffusion. By analyzing the distributions of the eigenvalues of the system and applying the center manifold theory and normal form computation, we show that, regarding the connection coefficients as the perturbation parameter, the system, with the different boundary conditions, undergoes some bifurcations including transcritical bifurcation, Hopf bifurcation and Hopf-zero bifurcation. The normal forms are given to determine the stabilities of the bifurcated solutions.

Keywords:

Neural network; Diffusion; Hopf bifurcation; Transcritical bifurcation; Interaction of Hopf bifurcation and Transcritical bifurcation.

Mathematics Subject Classification: Primary: 35B32, 37G05; Secondary: 37G10.

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