Journal of Applied Mathematics

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

Yingguo Li

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 357382, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495014

Digital Object Identifier
doi:10.1155/2012/357382

Mathematical Reviews number (MathSciNet)
MR2872350

Zentralblatt MATH identifier
1235.93191

Citation

Li, Yingguo. Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay. J. Appl. Math. 2012 (2012), Article ID 357382, 13 pages. doi:10.1155/2012/357382. https://projecteuclid.org/euclid.jam/1355495014


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