Abstract and Applied Analysis
Volume 2011 (2011), Article ID 697630, 21 pages
http://dx.doi.org/10.1155/2011/697630
Research Article

Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms

Changjin Xu1 and Xiaofei He2

1Guizhou Key Laboratory of Economics System Simulation, Guizhou College of Finance and Economics, Guiyang 550004, China
2Department of Mathematics, Zhangjiajie College of jishou University, Zhangjiajie 427000, China

Received 8 January 2011; Revised 27 February 2011; Accepted 27 April 2011

Academic Editor: Nobuyuki Kenmochi

Copyright © 2011 Changjin Xu and Xiaofei He. 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.

Abstract

A class of two-neuron networks with resonant bilinear terms is considered. The stability of the zero equilibrium and existence of Hopf bifurcation is studied. It is shown that the zero equilibrium is locally asymptotically stable when the time delay is small enough, while change of stability of the zero equilibrium will cause a bifurcating periodic solution as the time delay passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out.