Hardcover ISBN:  9780821849453 
Product Code:  GSM/118 
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Electronic ISBN:  9781470411800 
Product Code:  GSM/118.E 
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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 infinitedimensional as well as to finitedimensional dynamical systems, and to discretetime as well as to continuoustime semiflows.
This monograph provides a selfcontained 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 timeheterogeneous persistence results are developed using socalled “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 metapopulation and discretetime nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinitedimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an agestructured model of cells growing in a chemostat.ReadershipGraduate students and research mathematicians interested in dynamical systems and mathematical biology.

Table of Contents

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


Additional Material

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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 infinitedimensional as well as to finitedimensional dynamical systems, and to discretetime as well as to continuoustime semiflows.
This monograph provides a selfcontained 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 timeheterogeneous persistence results are developed using socalled “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 metapopulation and discretetime nonlinear matrix models of demographic dynamics. Entire chapters are devoted to infinitedimensional examples including an SI epidemic model with variable infectivity, microbial growth in a tubular bioreactor, and an agestructured 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