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Canards in a bottleneck
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Iuorio, Annalisa, Jankowiak, Gaspard, Szmolyan, Peter and Wolfram, Marie-Therese (2023) Canards in a bottleneck. Physica D: Nonlinear Phenomena, 451 . 133768. doi:10.1016/j.physd.2023.133768 ISSN 0167-2789.
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Official URL: http://doi.org/10.1016/j.physd.2023.133768
Abstract
In this paper, we investigate the stationary profiles of a nonlinear Fokker–Planck equation with small diffusion and nonlinear inflow and outflow boundary conditions. We consider corridors with a bottleneck whose width has a unique global nondegenerate minimum in the interior. In the small diffusion limit, the profiles are obtained constructively by using methods from geometric singular perturbation theory (GSPT). We identify three main types of profiles corresponding to: (i) high density in the domain and a boundary layer at the entrance, (ii) low density in the domain and a boundary layer at the exit, and (iii) transitions from high density to low density inside the bottleneck with boundary layers at the entrance and exit. Interestingly, solutions of the last type involve canard solutions generated at the narrowest point of the bottleneck. We obtain a detailed bifurcation diagram of these solutions in terms of the inflow and outflow rates. The analytic results based on GSPT are further corroborated by computational experiments investigating corridors with bottlenecks of variable width.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Fokker-Planck equation, Differential equations, Nonlinear -- Numerical solutions | ||||||||
Journal or Publication Title: | Physica D: Nonlinear Phenomena | ||||||||
Publisher: | Elsevier BV | ||||||||
ISSN: | 0167-2789 | ||||||||
Official Date: | September 2023 | ||||||||
Dates: |
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Volume: | 451 | ||||||||
Article Number: | 133768 | ||||||||
DOI: | 10.1016/j.physd.2023.133768 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 31 May 2023 | ||||||||
Date of first compliant Open Access: | 31 May 2023 | ||||||||
RIOXX Funder/Project Grant: |
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