Spreading Speeds in Slowly Oscillating Environments View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2010-07

AUTHORS

François Hamel, Julien Fayard, Lionel Roques

ABSTRACT

In this paper, we derive exact asymptotic estimates of the spreading speeds of solutions of some reaction-diffusion models in periodic environments with very large periods. Contrarily to the other limiting case of rapidly oscillating environments, there was previously no explicit formula in the case of slowly oscillating environments. The knowledge of these two extremes permits to quantify the effect of environmental fragmentation on the spreading speeds. On the one hand, our analytical estimates and numerical simulations reveal speeds which are higher than expected for Shigesada-Kawasaki-Teramoto models with Fisher-KPP reaction terms in slowly oscillating environments. On the other hand, spreading speeds in very slowly oscillating environments are proved to be 0 in the case of models with strong Allee effects; such an unfavorable effect of aggregation is merely seen in reaction-diffusion models. More... »

PAGES

1166-1191

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11538-009-9486-7

DOI

http://dx.doi.org/10.1007/s11538-009-9486-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1017058824

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/20091355


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59 schema:description In this paper, we derive exact asymptotic estimates of the spreading speeds of solutions of some reaction-diffusion models in periodic environments with very large periods. Contrarily to the other limiting case of rapidly oscillating environments, there was previously no explicit formula in the case of slowly oscillating environments. The knowledge of these two extremes permits to quantify the effect of environmental fragmentation on the spreading speeds. On the one hand, our analytical estimates and numerical simulations reveal speeds which are higher than expected for Shigesada-Kawasaki-Teramoto models with Fisher-KPP reaction terms in slowly oscillating environments. On the other hand, spreading speeds in very slowly oscillating environments are proved to be 0 in the case of models with strong Allee effects; such an unfavorable effect of aggregation is merely seen in reaction-diffusion models.
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