Electron. J. Diff. Equ., Vol. 2013 (2013), No. 198, pp. 1-12.

Stability and bifurcation analysis for a discrete-time bidirectional ring neural network model with delay

Yan-Ke Du, Rui Xu, Qi-Ming Liu

Abstract:
We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.

Submitted January 3, 2012. Published September 5, 2013.
Math Subject Classifications: 92B20, 34K18, 34K20, 37G05.
Key Words: Neural network; time delay; stability; bifurcation.

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Yan-Ke Du
Institute of Applied Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang, 050003, China
email: yankedu2011@163.com
Rui Xu
Institute of Applied Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang, 050003, China
email: rxu88@163.com
Qi-Ming Liu
Institute of Applied Mathematics
Shijiazhuang Mechanical Engineering College
Shijiazhuang, 050003, China
email: lqmmath@163.com

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