Global existence of periodic solutions in a tri-neuron network model with delays

We consider a delayed differential system that models a network of three neurons with memory. Using a global Hopf bifurcation theorem for FDE due to J. Wu and a Bendixson’s criterion for high-dimensional ODE 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.