Persistence for a two-stage reaction-diffusion system
Author
dc.contributor.author
Cantrell, Robert Stephen
Author
dc.contributor.author
Cosner, Chris
Author
dc.contributor.author
Martínez Salazar, Salomé Minerva
Admission date
dc.date.accessioned
2020-09-08T19:52:24Z
Available date
dc.date.available
2020-09-08T19:52:24Z
Publication date
dc.date.issued
2020
Cita de ítem
dc.identifier.citation
Mathematics 2020, Vol.8, No.3: 396
es_ES
Identifier
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10.3390/math8030396
Identifier
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https://repositorio.uchile.cl/handle/2250/176721
Abstract
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In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model's predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around <mml:semantics>(0,0)</mml:semantics> and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case.
es_ES
Patrocinador
dc.description.sponsorship
National Science Foundation (NSF)
DMS 15-14792
18-53478
CONICYT + PIA/Concurso de Apoyo a Centros Científicos y Tecnológicos de Excelencia con Financiamiento Basal
AFB170001