@inproceedings{1a16d070efd94a4abf0a521707287063,

title = "Persistent Discrete-Time Dynamics on Measures",

abstract = "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.",

keywords = "Basic reproduction number, Eigenfunctions, Extinction, Feller kernel, Flat norm (also known as dual bounded lipschitz norm)",

author = "Thieme, {Horst R.}",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.; 25th International Conference on Difference Equations and Applications, ICDEA 2019 ; Conference date: 24-06-2019 Through 28-06-2019",

year = "2020",

doi = "10.1007/978-3-030-60107-2_4",

language = "English (US)",

isbn = "9783030601065",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "59--100",

editor = "Steve Baigent and Martin Bohner and Saber Elaydi",

booktitle = "Progress on Difference Equations and Discrete Dynamical Systems - 25th ICDEA, 2019",

}