Relaxation oscillations and canard solutions in singular systems on the plane

Under study are the relaxation oscillations and canard solutions in singularly perturbed systems of ordinary differential equations with one slow and one fast variable. The study is based on application of classical mathematics and elements of infinitesimal calculus. A condition is given under which the relaxation oscillation is considered as the limit position of a family of canards under the tendency to zero of the repelling part of the slow manifold to which some parts of the canard trajectories of the family are infinitesimally close. © 2010 Pleiades Publishing, Ltd.