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Softcover ISBN:  9781470474652 
Product Code:  SURV/281 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470477349 
Product Code:  SURV/281.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470474652 
eBook ISBN:  9781470477349 
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 

Book DetailsMathematical Surveys and MonographsVolume: 281; 2024MSC: Primary 37; 39; 47; 92; Secondary 28; 46
A fundamental question in the theory of discrete and continuoustime 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 firstorder 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 discretetime 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 orderpreserving 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.
ReadershipGraduate students and researchers interested in the theory of discretetime 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

Orderbounded 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 rankstructured population with mating

Two diffusing sexes and short reproductive season

Nonlocal spatial spread of semelparous twosex populations

Populations with measurevalued structural distributions

Appendix A. Some tools from real analysis

Bibliography

Index


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A fundamental question in the theory of discrete and continuoustime 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 firstorder 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 discretetime 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 orderpreserving 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.
Graduate students and researchers interested in the theory of discretetime 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

Orderbounded 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 rankstructured population with mating

Two diffusing sexes and short reproductive season

Nonlocal spatial spread of semelparous twosex populations

Populations with measurevalued structural distributions

Appendix A. Some tools from real analysis

Bibliography

Index