Stability and hopf bifurcation of a delayed network of four neurons with a short-cut connection

This paper reveals the dynamics of a delayed neural network of four neurons, with a short-cut connection through a theoretical analysis and some case studies of both numerical simulations and experiments. It presents a detailed analysis of the stability and the stability switches of the network equilibrium, as well as the Hopf bifurcation and the bifurcating periodic responses on the basis of the normal form and the center manifold reduction. Afterwards, the study focuses on the validation of theoretical results through numerical simulations and circuit experiments. The numerical simulations and the circuit experiments not only show good agreement with theoretical results, but also show abundant effects of the short-cut connection on the network dynamics.