Stability and Hopf bifurcation of a delayed Cohen-Grossberg neural network with diffusion

详细信息    查看全文

• 作者：Xiaohong Tian and Rui Xu
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：293-305
• 全文大小：446K
• ISSN：1099-1476

文摘

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