AI Article Synopsis
- The paper presents exact asymptotic estimates of spreading speeds in reaction-diffusion models within periodic environments that have large periods, filling a gap in previous research on slowly oscillating environments.
- Findings indicate that the spreading speeds in slowly oscillating environments are unexpectedly higher for certain models compared to the anticipated speeds from Shigesada-Kawasaki-Teramoto models.
- Additionally, it is established that in very slowly oscillating environments, the spreading speeds can reduce to zero due to strong Allee effects, highlighting the unique impact of environmental fragmentation on these models.
Article 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.
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| http://dx.doi.org/10.1007/s11538-009-9486-7 | DOI Listing |
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