Geodesic
Self-oscillations in implicit singularly perturbed dynamical systems on~the~plane
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 157-176

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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. 
@article{ND_2014_10_2_a2,
     author = {Vladimir V. Gotsulenko},
     title = {Self-oscillations in implicit singularly perturbed dynamical systems on~the~plane},
     journal = {Russian journal of nonlinear dynamics},
     pages = {157--176},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_2_a2/}
}
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Vladimir V. Gotsulenko. Self-oscillations in implicit singularly perturbed dynamical systems on~the~plane. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 2, pp. 157-176. http://geodesic.mathdoc.fr/item/ND_2014_10_2_a2/