Vladimir Gotsulenko

    2a Zhelyabov, Kiev, 03680, Ukraine
    National Academy of Sciences of Ukraine Institute of Engineering Thermophysics


    Gotsulenko V. V.
    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.
    Keywords: implicitly singularly perturbed system, sliding mode, the relaxation periodic solution, self-oscillations
    Citation: Gotsulenko V. V.,  Self-oscillations in implicit singularly perturbed dynamical systems on the plane, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  157-175

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