Persistence of discrete dynamical systems in infinite dimensional state spaces
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.
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2014
Agent
- Author (aut): Jin, Wen
- Thesis advisor (ths): Thieme, Horst
- Committee member: Milner, Fabio
- Committee member: Quigg, John
- Committee member: Smith, Hal
- Committee member: Spielberg, John
- Publisher (pbl): Arizona State University