Hopf bifurcation analysis of a four-neuron network with multiple time delays

This paper reveals the dynamics of a neural network of four neurons with multiple time delays and a short-cut connection through a combined study of theoretical analysis, numerical simulations, and experiments. The first step of the study is to derive the sufficient conditions for the stability and instability of the network equilibrium, and the second step is to determine the properties of the periodic response bifurcating from a Hopf bifurcation of the network equilibrium on the basis of the normal form and the center manifold reduction. Afterwards, the study turns to the validation of theoretical results through numerical simulations and a circuit experiment. The case studies show that both numerical simulations and circuit experiment get a nice agreement with theoretical results.