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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
 
Horst R. Thieme Arizona State University, Tempe, AZ
Softcover ISBN:  978-1-4704-7465-2
Product Code:  SURV/281
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
eBook ISBN:  978-1-4704-7734-9
Product Code:  SURV/281.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7465-2
eBook: ISBN:  978-1-4704-7734-9
Product Code:  SURV/281.B
List Price: $260.00 $197.50
MAA Member Price: $234.00 $177.75
AMS Member Price: $208.00 $158.00
Not yet published - Preorder Now!
Expected availability date: June 08, 2024
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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators
Horst R. Thieme Arizona State University, Tempe, AZ
Softcover ISBN:  978-1-4704-7465-2
Product Code:  SURV/281
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
eBook ISBN:  978-1-4704-7734-9
Product Code:  SURV/281.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7465-2
eBook ISBN:  978-1-4704-7734-9
Product Code:  SURV/281.B
List Price: $260.00 $197.50
MAA Member Price: $234.00 $177.75
AMS Member Price: $208.00 $158.00
Not yet published - Preorder Now!
Expected availability date: June 08, 2024
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2812024
    MSC: Primary 37; 39; 47; 92; Secondary 28; 46

    A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence.

    This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive.

    While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

    Readership

    Graduate students and researchers interested in the theory of discrete-time dynamical systems with applications in population dynamics.

  • Table of Contents
     
     
    • Introduction
    • Cones and ordered vector spaces
    • The ordered vector space of real measures
    • Homogeneous operators
    • Spectral radii for homogeneous operators
    • Order-bounded operators
    • Upper semicontinuity of spectral radii
    • A left resolvent for homogeneous operators
    • Eigenvectors of (pseudo-)compact homogeneous operators
    • Continuity of the spectral radius
    • Eigenfunctionals
    • Turnover versus reproduction number
    • Linear maps on the vector space of measures
    • Nonlinear dynamics
    • Unstructured population models
    • A rank-structured population with mating
    • Two diffusing sexes and short reproductive season
    • Nonlocal spatial spread of semelparous two-sex populations
    • Populations with measure-valued structural distributions
    • Appendix A. Some tools from real analysis
    • Bibliography
    • Index
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2812024
MSC: Primary 37; 39; 47; 92; Secondary 28; 46

A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence.

This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive.

While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Readership

Graduate students and researchers interested in the theory of discrete-time dynamical systems with applications in population dynamics.

  • Introduction
  • Cones and ordered vector spaces
  • The ordered vector space of real measures
  • Homogeneous operators
  • Spectral radii for homogeneous operators
  • Order-bounded operators
  • Upper semicontinuity of spectral radii
  • A left resolvent for homogeneous operators
  • Eigenvectors of (pseudo-)compact homogeneous operators
  • Continuity of the spectral radius
  • Eigenfunctionals
  • Turnover versus reproduction number
  • Linear maps on the vector space of measures
  • Nonlinear dynamics
  • Unstructured population models
  • A rank-structured population with mating
  • Two diffusing sexes and short reproductive season
  • Nonlocal spatial spread of semelparous two-sex populations
  • Populations with measure-valued structural distributions
  • Appendix A. Some tools from real analysis
  • Bibliography
  • Index
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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