Geodesic
Conditions for existence of relaxation oscillations in singular systems of low dimension
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 87-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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Relaxation oscillations are studied in a singularly perturbed system of ordinary differential equations with $m$ slow and $n$ fast variables for the case of $m=2$ and $n=1$. Necessary conditions and sufficient conditions for existence of relaxation oscillations are given. 
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L. I. Kononenko. Conditions for existence of relaxation oscillations in singular systems of low dimension. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 3, pp. 87-92. http://geodesic.mathdoc.fr/item/SJIM_2005_8_3_a9/

[1] Andronov A. A., Vitt A. A., Khaikin S. E., Teoriya kolebanii, Nauka, M., 1981 | MR | Zbl

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

[3] Zvonkin A. K., Shubin M. A., “Nestandartnyi analiz i singulyarnye vozmuscheniya”, Uspekhi mat. nauk, 39:2(236) (1984), 77–127 | MR | Zbl

[4] Kononenko L. I., “Relaksatsionnye kolebaniya v singulyarnykh sistemakh s medlennymi i bystrymi peremennymi”, Sib. zhurn. industr. matematiki, 7:3(19) (2004), 102–110 | MR | Zbl

[5] Goldshtein V. M., Sobolev V. A., Kachestvennyi analiz singulyarno vozmuschennykh sistem, izd. In-ta matematiki SO AN SSSR, Novosibirsk, 1988

[6] Sobolev V. A., Schepakina E. A., “Integralnye poverkhnosti so smenoi ustoichivosti”, Izv. RAEN. Ser. MMMiU, 1:3 (1997), 151–175 | MR | Zbl

[7] Kononenko L. I., “Infinitezimalnyi analiz singulyarnykh sistem s bystrymi i medlennymi peremennymi”, Sib. zhurn. industr. matematiki, 6:4(16) (2003), 51–59 | MR | Zbl

[8] Rotstein H. G., Kopell N., Zhabotinsky A. M., Epstein I. R., “A canard mechanism for localization in systems of globally coupled oscillators”, SIAM J. Appl. Math., 63:6 (2003), 1998–2019 | DOI | MR | Zbl

[9] Chen X., Yu P., Han M., Zhang W., “Canard solution of two-demensional singularly perturbed systems”, Chaos. Solitons Fractals, 23 (2005), 915–927 | DOI | MR | Zbl

[10] Kononenko L. I., “O gladkosti medlennykh poverkhnostei singulyarno vozmuschennykh sistem”, Sib. zhurn. industr. matematiki, 5:2(10) (2002), 109–125 | MR | Zbl