Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations
type: Item
instance of: scholarly article
title: Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations
zbMATH Open document ID: 0823.92022
author: Ryszard Rudnicki
author: M. C. Mackey
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-10-31T00:00:00Z
review text: Here we examine the limiting growth characteristics of a multistage age- structured population of the type considered by \textit{H. Inaba} [Math. Popul. Stud. 1, 49 - 77 (1988)]. We prove a theorem on weak ergodicity of nonautonomous populations. This theorem generalizes Inaba's results concerning weak ergodicity [Math. Biosci. 96, No. 2, 195 - 219 (1989; Zbl 0698.92020)] and strong ergodicity. The method of proof is based on ideas similar to Inaba. However, we restrict our investigation to a space of real-valued bounded functions with the supremum norm. This allows us to omit the lattice-theoretic apparatus used by Inaba in his 1989 - paper. The plan of the paper is as follows. In Section 2 we precisely formulate the problem, while Section 3 introduces the property of asymptotic similarity. The notion of asymptotic similarity describes the same features of the multiplicative process was weak ergodicity, but in our case it is more convenient. Section 4 presents our main result on the growth properties of the system, and this result is proved in Section 5. Finally, Section 6 considers both autonomous and nonautonomous growth properties using that main result.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35F15
Mathematics Subject Classification ID: 60K99
zbMATH DE Number: 703345
zbMATH Keywords: transport equation
zbMATH Keywords: multistage age-structured population
zbMATH Keywords: weak ergodicity of nonautonomous populations
zbMATH Keywords: asymptotic similarity
zbMATH Keywords: multiplicative process
zbMATH Keywords: autonomous
zbMATH Keywords: nonautonomous
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1374
OpenAlex ID: W2075335373
DOI: 10.1006/JMAA.1994.1374
description: scientific article; zbMATH DE number 703345