Simple zero singularity analysis in a coupled FitzHugh–Nagumo neural system with delay

A FitzHugh–Nagumo (FHN) model with delayed coupling is considered to investigate the steady state bifurcation due to the coupling strength and delay. The center manifold reduction and normal form method are employed to study the bifurcation from zero singularity. We show that the coupling strength can induce both the pitchfork and transcritical bifurcations and the coupled delay has the most significant impact on these bifurcations. An example is applied to display the above results. Our investigation will contribute to the understanding of the influence of the time delay in signal transmission on the dynamics of coupled neurons.