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Nelin. Dinam., 2014, Volume 10, Number 2, Pages 157–176 (Mi nd433)  

Self-oscillations in implicit singularly perturbed dynamical systems on the plane

Vladimir V. Gotsulenko

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

Abstract: 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.

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UDC: 530.182
MSC: 39A23, 39A33
Received: 29.01.2014
Revised: 04.03.2014

Citation: Vladimir V. Gotsulenko, “Self-oscillations in implicit singularly perturbed dynamical systems on the plane”, Nelin. Dinam., 10:2 (2014), 157–176

Citation in format AMSBIB
\Bibitem{Got14}
\by Vladimir~V.~Gotsulenko
\paper Self-oscillations in implicit singularly perturbed dynamical systems on~the~plane
\jour Nelin. Dinam.
\yr 2014
\vol 10
\issue 2
\pages 157--176
\mathnet{http://mi.mathnet.ru/nd433}


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