2a Zhelyabov, Kiev, 03680, Ukraine
National Academy of Sciences of Ukraine Institute of Engineering Thermophysics
Gotsulenko V. V.
Self-oscillations in implicit singularly perturbed dynamical systems on the plane
2014, Vol. 10, No. 2, pp. 157-175
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.