Description
ORIENT BLACKSWAN Dynamical Systems And Population Persistence 1905 Edition by Hal L. Smith
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. 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 BibliographyIndex