Persistent Discrete-Time Dynamics on Measures

Horst R. Thieme

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


A discrete-time structured population model is formulated by a population turnover map F on the cone of finite nonnegative Borel measures that maps the structural population distribution of a given year to the one of the next year. F has a first order approximation at the zero measure (the extinction fixed point), which is a positive linear operator on the ordered vector space of real measures and can be interpreted as a basic population turnover operator. A spectral radius can be defined by the usual Gelfand formula and can be interpreted as basic population turnover number. We continue our investigation (Thieme, H.R.: Discrete-time population dynamics on the state space of measures, Math. Biosci. Engin. 17:1168–1217 (2020). doi: 10.3934/mbe.2020061) in how far the spectral radius serves as a threshold parameter between population extinction and population persistence. Emphasis is on conditions for various forms of uniform population persistence if the basic population turnover number exceeds 1.

Original languageEnglish (US)
Title of host publicationProgress on Difference Equations and Discrete Dynamical Systems - 25th ICDEA, 2019
EditorsSteve Baigent, Martin Bohner, Saber Elaydi
Number of pages42
ISBN (Print)9783030601065
StatePublished - 2020
Event25th International Conference on Difference Equations and Applications, ICDEA 2019 - London, United Kingdom
Duration: Jun 24 2019Jun 28 2019

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference25th International Conference on Difference Equations and Applications, ICDEA 2019
Country/TerritoryUnited Kingdom


  • Basic reproduction number
  • Eigenfunctions
  • Extinction
  • Feller kernel
  • Flat norm (also known as dual bounded lipschitz norm)

ASJC Scopus subject areas

  • Mathematics(all)


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