Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013, Special Issue (2013), Article ID 367589, 9 pages.
Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation
The dynamics of a 2-dimensional neural network model in neutral form are investigated. We prove that a sequence of Hopf bifurcations occurs at the origin as the delay increases. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using normal form method and center manifold theory. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. Finally, some numerical simulations are carried out to support the analytic results.
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 367589, 9 pages.
First available in Project Euclid: 26 February 2014
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Liu, Ming; Xu, Xiaofeng. Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 367589, 9 pages. doi:10.1155/2013/367589. https://projecteuclid.org/euclid.aaa/1393449627