Stability of steady state and boundedness of a 2-sex population model
type: Item
instance of: scholarly article
title: Stability of steady state and boundedness of a 2-sex population model
zbMATH Open document ID: 0954.92021
DOI: 10.1016/S0362-546X(98)00230-2
author: C. O. A. Sowunmi
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-02-15T00:00:00Z
review text: This study resumes/continues the author's previous concerns for establishing a realistic model, capable of rendering the contribution of both sexes to the reproduction process (on excluding monogamy or the dominance of either sex). The two essential concepts involved in the regulation of population(al) growth are boundedness and stability of equilibria. Once established the contributions brought by both sexes to the reproduction process, the author directs his researches towards the mode in which the demands of boundedness and/or stability affect the male and female species. The model employed for the ample demonstrations that follow is that of a heterosexual population, including three main classes: male, non-gestating female and gestating female, the first two classes being further sub-divided into pre-reproductive, reproductive and post-reproductive ones. Another section, entitled ``sufficient conditions for bounded populations'', tries to solve the following problem: how could the parameters be related if a population is not to exceed a pre-determined value, while the paragraph ``Sufficient conditions for asymptotic stability of a steady state'' analyses them in the idea that stability may assure populations' regulation.
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1419541
zbMATH Keywords: boundedness
zbMATH Keywords: equilibrium
zbMATH Keywords: reproduction process
zbMATH Keywords: male
zbMATH Keywords: female
zbMATH Keywords: asymptotic stability
reviewed by: Cristina Irimia
MaRDI profile type: Publication
cites work: Non-linear age-dependent population dynamics
cites work: A model of heterosexual population dynamics with age structure and gestation period
full work available at URL: s0362-546x(98)00230-2
OpenAlex ID: W2084355351
description: scientific article; zbMATH DE number 1419541