On solutions related to FitzHugh-Rinzel type model

Abstract

A ternary autonomous dynamical system of FitzHugh-Rinzel type is analyzed. The system, at start, is reduced to a nonlinear integro differential equation. The fundamental solution $ H(x,t) $ is explicitly determined and the initial value problem is analyzed in the whole space. The solution is expressed by means of an integral equation involving $ H(x,t) $. Moreover, adding an extra control term, explicit solutions are achieved.