The Book
The mathematical theory of persistence answers questions such as which species, in a mathematical model of interacting species, will survive over the long term. It applies to infinite-dimensional as well as to finite-dimensional dynamical systems, and to discrete-time as well as to continuous-time semiflows. This book provides a self-contained treatment of persistence theory that is accessible to graduate students. Applications play a large role from the beginning. These include ODE models such as SEIRS infectious disease in a meta-population and discrete-time nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinite-dimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an age-structured model of cells growing in a chemostat.
The Author(s)
Hal L Smith is Professor at the School of Mathematical and Statistical Sciences, College of Liberal Arts and Sciences, Arizona State University, Tempe, USA.
Horst R Thieme is Professor at the School of Mathematical and Statistical Sciences, College of Liberal Arts and Sciences, Arizona State University, Tempe, USA.
Table of Contents
Preface
Chapter 1. Semiflows on Metric Spaces
Chapter 2. Compact Attractors
Chapter 3. Uniform Weak Persistence
Chapter 4. Uniform Persistence
Chapter 5. The Interplay of Attractors, Repellers, and Persistence
Chapter 6. Existence of Nontrivial Fixed Points via Persistence
Chapter 7. Nonlinear Matrix Models: Main Act
Chapter 8. Topological Approaches to Persistence
Chapter 9. An SI Endemic Model with Variable Infectivity
Chapter 10. Semiflows Induced by Semilinear Cauchy Problems
Chapter 11. Microbial Growth in a Tubular Bioreactor
Chapter 12. Dividing Cells in a Chemostat
Chapter 13. Persistence for Nonautonomous Dynamical Systems
Chapter 14. Forced Persistence in Linear Cauchy Problems
Chapter 15. Persistence via Average Lyapunov Functions
Appendix A. Tools from Analysis and Differential Equations
Appendix B. Tools from Functional Analysis and Integral Equations
Bibliography
Index