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Stability and Hopf bifurcation of a delayed reaction–diffusion neural network

✍ Scribed by Qintao Gan; Rui Xu

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
355 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

In this paper, a delayed reaction-diffusion neural network with

Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed. The existence of Hopf bifurcation at the trivial steady state is established. Using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae are derived to determine the direction and stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

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