Parameterization and qualitative analysis of a~singular system in a~mathematical model of catalytic oxidation
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 44-52.

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We qualitatively analyze the slow subsystem on one sheet of a parameterized slow surface and, as a result, justify the possibility of duck solutions.
Keywords: mathematical modeling, singularly perturbed systems.
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L. I. Kononenko; E. P. Volokitin. Parameterization and qualitative analysis of a~singular system in a~mathematical model of catalytic oxidation. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 1, pp. 44-52. http://geodesic.mathdoc.fr/item/SJIM_2012_15_1_a4/

[1] Boronin A. I., Nizovskii A. I., Elokhin V. I., Yablonskii G. S., Savchenko V. I., “Eksperimentalnoe obosnovanie mekhanizma reaktsii $\mathrm{CO}_2$ na iridii i ego chislennoe modelirovanie”, Tez. dokl. 4 Vsesoyuz. konf. po mekhanizmu kataliticheskikh reaktsii, Ch. 2, M., 1996, 196–200

[2] Gainova I. A., Fadeev S. I., Elokhin V. I., Boronin A. I., “Reaktsiya okisleniya $\mathrm{CO}$ na polikristallicheskoi folge iridiya”, Modelirovanie kinetiki poverkhnostnykh protsessov, Tr. Mezhdunar. konf. po vychislitelnoi matematike. Ch. 1, Novosibirsk, 2004, 449–454

[3] Kononenko L. I., Integralnye mnogoobraziya v matematicheskoi modeli reaktsii kataliticheskogo okisleniya, Preprint No 13, In-t matematiki SO AN SSSR, Novosibirsk, 1990, 43 pp.

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

[5] Mitropolskii Yu. A., Lykova O. B., Integralnye mnogoobraziya v nelineinoi mekhanike, Nauka, M., 1963 | MR

[6] Vasileva A. V., Butuzov V. F., Singulyarno vozmuschennye uravneniya v kriticheskikh sluchayakh, Izd-vo MGU, M., 1978 | MR

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

[8] Kononenko L. I., “Parametrizatsiya medlennoi krivoi v odnoi zadache khimicheskoi kinetiki”, Sib. zhurn. industr. matematiki, 13:3(43) (2010), 51–57 | MR | Zbl

[9] Arnold V. I., Afraimovich V. S., Ilyashenko Yu. S., Shilnikov L. P., “Teoriya bifurkatsii”, Itogo nauki i trekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 5, VINITI, M., 1986, 5–218 | MR | Zbl

[10] Tikhonov A. N., “O zavisimosti reshenii differentsialnykh uravnenii ot malogo parametra”, Mat. sbornik, 22(64):2 (1948), 193–204 | MR | Zbl

[11] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Mat. sbornik, 31(73):3 (1952), 575–586 | MR | Zbl

[12] Callot J.-L., Diener F., Diener M., “Le probléme de la ‘chasse an canard’ ”, C. R. Acad. Sci. Sér. 1, 286:22 (1978), 1059–1061 | MR

[13] Chumakov G. A., Chumakova N. A., “Relaxation oscillations in a kinetic model of catalytic hydrogen oxidation involving a chase on canards”, Chem. Engrg. J., 91:2–3 (2003), 151–158 | DOI

[14] Kononenko L. I., “Relaksatsii v singulyarno vozmuschennykh sistemakh na ploskosti”, Vestnik NGU. Ser. Matematika, mekhanika, informatika, 9:4 (2009), 45–50

[15] Krupa M., Shmolyan P., “Relaxation oscillations and canard explosion”, J. Differential Equations, 174 (2001), 312–368 | DOI | MR | Zbl

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

[17] Bobkova A. S., Kolesov A. Yu., Rozov N. Kh., “Problema “vyzhivaniya utok” v trekhmernykh singulyarno vozmuschennykh sistemakh s dvumya medlennymi peremennymi”, Mat. zametki, 71:6 (2002), 818–831 | MR | Zbl

[18] Sobolev V. A., Schepakina E. A., “Traektorii-utki v odnoi zadache teorii goreniya”, Differents. uravneniya, 32:9 (1996), 1175–1184 | MR | Zbl

[19] Sobolev V. A., Schepakina E. A., “Integralnye poverkhnosti so smenoi ustoichivosti i traektorii-utki”, Izv. RAEN. Ser. MMMIU, 1:3 (1997), 176–187

[20] Wechselberger M., “Canards”, Scholarpedia, 2:4 (2007), 1356 | DOI