This article is cited in 5 papers

On immediate-delayed exchange of stabilities and periodic forced canards

N. N. Nefedov^a, K. R. Schneider<sup>b

a</sup> 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.

UDC: 519.624.2

Received: 12.01.2007
Revised: 02.07.2010

Language: English

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

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