Details

Subject(s)

• Population biology—Mathematical models [Browse]
• Discrete-time systems [Browse]
• Difference equations [Browse]
• Integral operators [Browse]
• Vector spaces [Browse]

Series

• Mathematical surveys and monographs ; v. 281. [More in this series]
• Mathematical surveys and monographs, 0076-5376 ; volume 281 [More in this series]

Summary note

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 dgree one) and order-preserving 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.

Bibliographic references

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
• 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 reproduction season
• Nonlocal spatial spread of semelparous two-sex populations
• Populations with measure-valued structural distributions.

Show 15 more Contents items

ISBN

• 9781470474652 (paperback)
• 1470474654 (paperback)

LCCN

2024002996

OCLC

1425892921

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