abstract: Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular models: a size-structured plant population model, a diffusion model (with both Neumann and Dirichlet boundary conditions) for a dispersing population of males and females that only mate and reproduce once during a very short season, and a rank-structured model for a population of males and females. / Dissertation/Thesis / Ph.D. Mathematics 2014
| Identifer | oai:union.ndltd.org:asu.edu/item:24874 |
| Date | January 2014 |
| Contributors | Jin, Wen (Author), Thieme, Horst (Advisor), Milner, Fabio (Committee member), Quigg, John (Committee member), Smith, Hal (Committee member), Spielberg, John (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 74 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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