Geodesic
The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 1-10 
A. Yu. Kolesov; E. F. Mishchenko. The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable. Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/SM_1991_70_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is assumed that the equilibrium state of the relaxation system $$ \varepsilon\dot x=f(x,y), \qquad \dot y=g(x,y,\mu), $$ where $x\in R^n$ and $y\in R$, passes generically through a point of discontinuity as $\mu$ varies. Under this condition stable duck cycles and cycles arising in a neighborhood of the equilibrium state are constructed.

[1] Mischenko E. F., Pontryagin L. S., “Periodicheskie resheniya sistem differentsialnykh uravnenii, blizkikh k razryvnym”, DAN SSSR, 102:5 (1955), 889–891 | Zbl

[2] Mischenko E. F., Rozov N. Kh., Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Nauka, M., 1975 | MR

[3] Kolesov A. Yu., Kolesov Yu. S, Mischenko E. F., Rozov N. Kh., “Asimptoticheskoe integrirovanie sistemy v variatsiyakh mnogomernogo relaksatsionnogo tsikla. I, II”, Differents. uravneniya, 23:11 (1987), 1412–1421 ; 12, 1571–1587 | MR

[4] Kolesov A. Yu., Kolesov Yu. S, Mischenko E. F., Rozov N. Kh., “Relaksatsionnaya sistema v okrestnosti tochki sryva: svedenie k regulyarnomu sluchayu”, UMN, 43:2 (1988), 141–142 | MR

[5] Kolesov A. Yu., Mischenko E. F., “Asimptotika relaksatsionnykh kolebanii”, Matem. sb., 137(179) (1988), 3–18

[6] Zvonkin A. K., Shubin M. A., “Nestandartnyi analiz i singulyarnye vozmuscheniya”, UMN, 39:2 (1984), 77–129 | MR

[7] Grasman J., Asymptotic methods for relaxation oscillations and applications, Applied Math. Sciences, 63, Springer, New York, 1987 | MR | Zbl

[8] Shishkova M. A., “Rassmotrenie odnoi sistemy differentsialnykh uravnenii s malym parametrom pri vysshikh proizvodnykh”, DAN SSSR, 209:3 (1973), 576–579 | Zbl

[9] Pontryagin L. S., Mischenko E. F., “Nekotorye voprosy teorii differentsialnykh uravnenii s malym parametrom”, Tr. MIAN, 169 (1985), 99–118 | MR

[10] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[11] Mitropolskii Yu. A., Lykova O. B., Integralnye mnogoobraziya v nelineinoi mekhanike, Nauka, M., 1973 | MR

[12] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1976 | MR