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Bifurcation analysis and existence of periodic solutions in a simple neural network with delays. (English) Zbl 1080.34064

Summary: Results are provided about the stability and bifurcation of periodic solutions for a (neural) network with n elements where delays between adjacent units and external inputs are included. The particular cases \(n = 2\) and \(n = 3\) are discussed in detail, to explicitly illustrate the role of the delays in the corresponding bifurcation sets and the stability properties, like a Hopf bifurcation, a pitchfork bifurcation, and a Bogdanov-Takens bifurcation.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
92B20 Neural networks for/in biological studies, artificial life and related topics
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