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Bifurcation analysis of a class of neural networks with delays. (English) Zbl 1156.37325
Summary: A class of n-dimensional neural network model with multi-delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation are obtained via employing the polynomial theorem to analyze the distribution of the roots of the associated characteristic equation. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the multiple stability is investigated and pitchfork bifurcation is also found. The results are illustrated by some numerical simulations.
MSC:
37N25Dynamical systems in biology
92B20General theory of neural networks (mathematical biology)
34K18Bifurcation theory of functional differential equations