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Spreading speeds in slowly oscillating environments.
Bull. Math. Biol. 72, 1166-1191 (2010)
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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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Spreading speeds; Reaction-diffusion; Fragmentation; Periodic environment; Allee effect
ISSN (print) / ISBN
0092-8240
e-ISSN
1522-9602
Journal
Bulletin of Mathematical Biology
Quellenangaben
Volume: 72,
Issue: 5,
Pages: 1166-1191
Publisher
Springer
Publishing Place
New York, NY
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)