A priori estimates for solutions of FitzHugh–Rinzel system

The FitzHugh–Rinzel system is able to describe some biophysical phenomena, such as bursting oscillations, and the study of its solutions can help to better understand several behaviours of the complex dynamics of biological systems. We express the solutions by means of an integral equation involving the fundamental solution H ( x , t ) related to a non linear integro-differential equation. Properties of H ( x , t ) allow us to obtain a priori estimates for solutions determined in the whole space, showing both the influence of the initial data and the source term.