Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators

Released on by Horst R. Thieme
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  • Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators Book Detail

  • Author : Horst R. Thieme
  • Release Date : 2024-05-07
  • Publisher : American Mathematical Society
  • Genre : Mathematics
  • Pages : 357
  • ISBN 13 : 1470474654
  • File Size : 14,14 MB
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Discrete-Time Dynamics of Structured Populations and Homogeneous Order-Preserving Operators by Horst R. Thieme PDF Summary

Book Description: 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.

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Positive Dynamical Systems in Discrete Time

Positive Dynamical Systems in Discrete Time

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This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables