Premium
Stability and Hopf bifurcation of a delayed Cohen–Grossberg neural network with diffusion
Author(s) -
Tian Xiaohong,
Xu Rui
Publication year - 2016
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.3995
Subject(s) - mathematics , center manifold , hopf bifurcation , neumann boundary condition , mathematical analysis , stability (learning theory) , bifurcation , partial differential equation , von neumann stability analysis , steady state (chemistry) , boundary value problem , nonlinear system , physics , chemistry , quantum mechanics , machine learning , computer science
In this paper, a delayed Cohen–Grossberg neural network with diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation at the trivial steady state are established, respectively. By using the normal form theory and the center manifold reduction of partial function differential equations, formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results. Copyright © 2016 John Wiley & Sons, Ltd.