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. 
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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/

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