Self-oscillations in implicit singularly perturbed dynamical systemson the plane
To implicitly singularly perturbed autonomous systems of ordinary diﬀerential equations of second order found some suﬃcient conditions for the existence of periodic solutions of relaxation (self-oscillation), determined by means of an auxiliary dynamical system that implements a sliding mode. It is shown that so deﬁned periodic motions have typical properties of self-oscillations of relaxation deﬁned autonomous systems of ordinary diﬀerential equations with a small parameter at the highest derivative.