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Bifurcation analysis in a neutral differential equation. (English) Zbl 1259.34061
Summary: The dynamics of a neural network model in neutral form is 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 the normal form method and center manifold theory. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. and a Bendixson’s criterion for higher-dimensional ordinary differential equations due to Li and Muldowney.

34K18Bifurcation theory of functional differential equations
34K40Neutral functional-differential equations
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
92B20General theory of neural networks (mathematical biology)
34K17Transformation and reduction of functional-differential equations and systems; normal forms
34K19Invariant manifolds (functional-differential equations)
Full Text: DOI
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