Zero singularities in a ring network with two delays (Q353368)

In this paper, a neural network model consisting of three neurons with delayed self- and nearest-neighbor connections is considered. Further, it is proved that the system undergoes multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the coupling coefficients as the bifurcation parameters, four kinds of zero singularities are demonstrated through center manifold reduction and normal form calculation. Numerical simulations are carried out to illustrate the main results.