Discretetime dynamics of structured populations and homogeneous orderpreserving operators
 Responsibility
 Horst R. Thieme.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2024]
 Physical description
 xii, 342 pages ; 26 cm.
 Series
 Mathematical surveys and monographs ; no. 281.
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Description
Creators/Contributors
 Author/Creator
 Thieme, Horst R., 1948 author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Cones and ordered vector spaces
 The ordered vector spaces 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 reproduction season
 Nonlocal spatial spread of semelparous twosex populations
 Populations with measurevalued structural distributions.
 Summary
 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 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 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 dgree one) and orderpreserving rather than linear and positive. While this book offers an introduction to ordered normal 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. Provided by publisher.
Subjects
Bibliographic information
 Publication date
 2024
 Series
 Mathematical surveys and monographs, 00765376 ; volume 281
 ISBN
 9781470474652 paperback
 1470474654 paperback
 9781470477349 electronic book