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Stability and Hopf bifurcation of a delayed reaction–diffusion neural network
Author(s) -
Gan Qintao,
Xu Rui
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1454
Subject(s) - mathematics , center manifold , hopf bifurcation , neumann boundary condition , reaction–diffusion system , mathematical analysis , stability (learning theory) , bifurcation , von neumann stability analysis , steady state (chemistry) , saddle node bifurcation , boundary value problem , nonlinear system , physics , quantum mechanics , machine learning , computer science , chemistry
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. Copyright © 2011 John Wiley & Sons, Ltd.