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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 1, Pages 46–61 (Mi zvmmf194)  
This article is cited in 5 scientific papers (total in 5 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
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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.
Received: 12.01.2007
Revised: 02.07.2010
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 1, Pages 43–58
DOI: https://doi.org/10.1007/s11470-008-1004-8
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: English
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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