On solutions related to FitzHugh-Rinzel typemodel

The FitzHugh-Rinzel system, a three dimensional non linear model able to describe bursting phenomena, is analyzed. The system is reduced to a nonlinear integro differential equation and the fundamental solution H(x; t) is explicitly determined. The initial value problem in all of the space is analyzed and the solution is achieved by means of an integral equation involving function H(x; t). Moreover, for particular value's constants that characterize the model's kinetic, explicit solutions of the FitzHugh-Rinzel system have been achieved.