Description
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.
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Title
- Persistence of discrete dynamical systems in infinite dimensional state spaces
Contributors
- Jin, Wen (Author)
- Thieme, Horst (Thesis advisor)
- Milner, Fabio (Committee member)
- Quigg, John (Committee member)
- Smith, Hal (Committee member)
- Spielberg, John (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2014
Subjects
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Note
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thesisPartial requirement for: Ph.D., Arizona State University, 2014
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bibliographyIncludes bibliographical references (p. 68-69)
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Field of study: Mathematics
Citation and reuse
Statement of Responsibility
by Wen Jin