Journal of Applied Mathematics
Volume 2012 (2012), Article ID 357382, 13 pages
Research Article

Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China

Received 14 August 2011; Revised 4 October 2011; Accepted 5 October 2011

Academic Editor: Shiping Lu

Copyright © 2012 Yingguo Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.