Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2011 (2011), Article ID 697630, 21 pages.
Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms
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.
Abstr. Appl. Anal., Volume 2011 (2011), Article ID 697630, 21 pages.
First available in Project Euclid: 12 August 2011
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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