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Global existence of periodic solutions in a tri-neuron network model with delays. (English) Zbl 1062.34077
Summary: We consider a delayed differential system that models a network of three neurons with memory. Using a global Hopf bifurcation theorem for FDEs due to J. Wu and a Bendixson’s criterion for high-dimensional ODEs due to Li and Muldowney, we obtain a group of sufficient conditions for the system to have multiple periodic solutions when the sum of delays is sufficiently large.

MSC:
34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
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