FOLDED SADDLE-NODES AND THEIR NORMAL FORM REDUCTION IN A NEURONAL RATE MODEL

The paper investigates the existence of folded singularities in a dynamical system of two fast and two slow equations. The normal formof the system near its fold curve is constructed. Then it is used todetermine the analytical conditions satisfied by a folded singularity.In particular, we find that there is a parameter region where foldedsaddle-nodes of type II exist. In the neighborhood of those points the system possesses a stable folded node and an unstable true equilibrium, and the local dynamics is complex.