Stability and Hopf bifurcation of a delayed Cohen–Grossberg neural network with diffusion |
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| Authors: | Xiaohong Tian Rui Xu |
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| Affiliation: | Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, China |
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| Abstract: | 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. |
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| Keywords: | Cohen– Grossberg neural network time delay diffusion stability Hopf bifurcation |
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