Document Server@UHasselt >
Research >
Research publications >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/9852

Title: Canards and bifurcation delays of spatially homogeneous and inhomogeneous types in reaction-diffusion equations
Authors: De Maesschalck, Peter
Popovic, Nikola
Kaper, Tasso J.
Issue Date: 2009
Citation: Advances in Differential Equations, 14(9-10). p. 943-962
Abstract: In ordinary differential equations of singular perturbation type, the dynamics of solutions near saddle-node bifurcations of equilibria are rich. Canard solutions can arise, which, after spending time near an attracting equilibrium, stay near a repelling branch of equilibria for long intervals of time before finally returning to a neighborhood of the attracting equilibrium (or of another attracting state). As a result, canard solutions exhibit bifurcation delay. In this article, we analyze some linear and nonlinear reaction-diffusion equations of singular perturbation type, showing that solutions of these systems also exhibit bifurcation delay and are, hence, canards. Moreover, it is shown for both the linear and the nonlinear equations that the exit time may be either spatially homogeneous or spatially inhomogeneous, depending on the magnitude of the diffusivity.
URI: http://hdl.handle.net/1942/9852
ISI #: 000275910500005
ISSN: 1079-9389
Category: A1
Type: Journal Contribution
Validation: ecoom, 2011
Appears in Collections: Research publications

Files in This Item:

Description SizeFormat
Preprint247.33 kBAdobe PDF

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.