Abstract and Applied Analysis

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

Changjin Xu and Xiaofei He

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 697630, 21 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171192

Digital Object Identifier
doi:10.1155/2011/697630

Mathematical Reviews number (MathSciNet)
MR2802842

Zentralblatt MATH identifier
1218.37122

Citation

Xu, Changjin; He, Xiaofei. Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms. Abstr. Appl. Anal. 2011 (2011), Article ID 697630, 21 pages. doi:10.1155/2011/697630. https://projecteuclid.org/euclid.aaa/1313171192


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