This work will extend recent work by Cronin on singularly perturbed equations which model a physiological system. The model, which is due to Noble, is a system of four nonlinear autonomous ordinary differential equations which describe the cardiac Purkinje fiber. The present research will use geometric analysis to determine intervals of parameter values for which the existence of a periodic solution can be established. The work will also consider other singularly perturbed equations in the areas of control and semiconductor theory for which the geometric approach is relevant.
