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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 1, Pages 46–61 (Mi zvmmf194)  

This article is cited in 3 scientific papers (total in 3 papers)

On immediate-delayed exchange of stabilities and periodic forced canards

N. N. Nefedova, K. R. Schneiderb

a Department of Mathematics, Faculty of Physics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
b Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin, Germany

Abstract: Singularly perturbed nonautonomous ordinary differential equations are studied for which the associated equations have equilibrium states consisting of at least two intersecting curves, which leads to exchange of stabilities of these equilibria. The asymptotic method of differential equations is used to derive conditions under which initial value problems have solutions characterized by immediate and delayed exchange of stabilities. These results are then used to prove the existence of periodic canard solutions.

Key words: singularly perturbed problems, differential inequalities, exchange of stabilities, internal layers.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:1, 43–58

Bibliographic databases:

UDC: 519.624.2
Received: 12.01.2007
Revised: 02.07.2010
Language:

Citation: N. N. Nefedov, K. R. Schneider, “On immediate-delayed exchange of stabilities and periodic forced canards”, Zh. Vychisl. Mat. Mat. Fiz., 48:1 (2008), 46–61; Comput. Math. Math. Phys., 48:1 (2008), 43–58

Citation in format AMSBIB
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    2. Mortell M.P., Shchepakina E., Sobolev V., “Singular Perturbations Introduction To System Order Reduction Methods With Applications Preface”: Shchepakina, E Sobolev, V Mortell, MP, Singular Perturbations: Introduction To System Order Reduction Methods With Applications, Lect. Notes Math., Lecture Notes in Mathematics, 2114, Springer-Verlag Berlin, 2014, IX+  mathscinet  isi
    3. Shchepakina E., “Calculation of Maximum Safe Temperature of Fuel'S Heating in a Porous Medium”, 3rd International Conference Information Technology and Nanotechnology (Itnt-2017), Procedia Engineering, 201, eds. Soifer V., Kazanskiy N., Korotkova O., Sazhin S., Elsevier Science BV, 2017, 468–477  crossref  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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