On a modification of the FitzHugh–Nagumo neuron model

A singularly perturbed system of ordinary differential equations with a fast and a slow variable is proposed, which is a modification of the well-known FitzHugh–Nagumo model from neuroscience. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a $\delta$-like function.