Geodesic
Relaxations in Singularly Perturbed Planar Systems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 45-50

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The relaxation oscilations and canard-solutions are studied in the system of singularly perturbed differential equations with one slow and one fast variables. The analysis is based on using classical mathematics, i.e., without elements of nonstandard analysis. The sufficient condition is presented for the fact that the relaxational oscillation is the limit position of the canard set as the repelling part of the slow manifold tends to zero.
Mots-clés : singular perturbations, relaxation oscilations, canard-solutions.
Keywords: slow and fast variables, slow surface 
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     author = {L. I. Kononenko},
     title = {Relaxations in {Singularly} {Perturbed} {Planar} {Systems}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {45--50},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a4/}
}
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L. I. Kononenko. Relaxations in Singularly Perturbed Planar Systems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 45-50. http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a4/