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Persistence of Discrete Dynamical Systems in Infinite Dimensional State Spaces

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

Identiferoai:union.ndltd.org:asu.edu/item:24874
Date January 2014
ContributorsJin, 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 SetsArizona State University
LanguageEnglish
Detected LanguageEnglish
TypeDoctoral Dissertation
Format74 pages
Rightshttp://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved

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