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

Pages: 367 - 376, Issue Special, September 2009

 Abstract        Full Text (183.2K)              

Rui Hu - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, Canada A1C 5S7, Canada (email)
Yuan Yuan - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, Canada A1C 5S7, Canada (email)

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

Received: July 2008;      Revised: July 2009;      Published: July 2009.