American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 367-376. doi: 10.3934/proc.2009.2009.367

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, Canada, Canada

Received  July 2008 Revised  July 2009 Published  July 2009

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.
Citation: Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367
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