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| Hardcover ISBN: | 978-0-8218-4945-3 |
| Product Code: | GSM/118 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-1180-0 |
| Product Code: | GSM/118.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-4945-3 |
| eBook ISBN: | 978-1-4704-1180-0 |
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| List Price: | $220.00 $177.50 |
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Book DetailsGraduate Studies in MathematicsVolume: 118; 2011; 405 ppMSC: Primary 37; 92
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 monograph provides a self-contained treatment of persistence theory that is accessible to graduate students. The key results for deterministic autonomous systems are proved in full detail such as the acyclicity theorem and the tripartition of a global compact attractor. Suitable conditions are given for persistence to imply strong persistence even for nonautonomous semiflows, and time-heterogeneous persistence results are developed using so-called “average Lyapunov functions”.
Applications play a large role in the monograph from the beginning. These include ODE models such as an 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.
ReadershipGraduate students and research mathematicians interested in dynamical systems and mathematical biology.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Semiflows on metric spaces
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Chapter 2. Compact attractors
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Chapter 3. Uniform weak persistence
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Chapter 4. Uniform persistence
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Chapter 5. The interplay of attractors, repellers, and persistence
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Chapter 6. Existence of nontrivial fixed points via persistence
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Chapter 7. Nonlinear matrix models: Main act
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Chapter 8. Topological approaches to persistence
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Chapter 9. An SI endemic model with variable infectivity
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Chapter 10. Semiflows induced by semilinear Cauchy problems
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Chapter 11. Microbial growth in a tubular bioreactor
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Chapter 12. Dividing cells in a chemostat
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Chapter 13. Persistence for nonautonomous dynamical systems
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Chapter 14. Forced persistence in linear Cauchy problems
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Chapter 15. Persistence via average Lyapunov functions
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Appendix A. Tools from analysis and differential equations
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Appendix B. Tools from functional analysis and integral equations
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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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 monograph provides a self-contained treatment of persistence theory that is accessible to graduate students. The key results for deterministic autonomous systems are proved in full detail such as the acyclicity theorem and the tripartition of a global compact attractor. Suitable conditions are given for persistence to imply strong persistence even for nonautonomous semiflows, and time-heterogeneous persistence results are developed using so-called “average Lyapunov functions”.
Applications play a large role in the monograph from the beginning. These include ODE models such as an 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.
Graduate students and research mathematicians interested in dynamical systems and mathematical biology.
-
Chapters
-
Introduction
-
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
