Reduced fertility and asymptotics of the logistic model

Daniel Maxin, Fabio Augusto Milner, Laurentiu M Sega

Research output: Contribution to journalArticle

Abstract

This logistic model includes three age groups. Juveniles do not reproduce, and old individuals reproduce at a lower rate. Pairings between individuals of different fertility rates may lead to multiple equilibria and bi-stability: the total population converges to different limits depending on its initial size. The behavior is correlated with transition rates from high to low fertility groups and with the frequency of pairing among the various groups of reproduction level. The proportions of adults at equilibrium are roots of a quartic polynomial, alternating sinks and saddles. Necessary and sufficient conditions for the existence of bi-stability are provided for a simplified model.

Original languageEnglish (US)
Pages (from-to)37-49
Number of pages13
JournalMathematical Population Studies
Volume23
Issue number1
DOIs
StatePublished - Jan 2 2016

Fingerprint

saddles
Birth Rate
logit analysis
Reproduction
Fertility
fertility
logistics
Age Groups
Logistic Models
fertility rate
Population
age group
Group
rate

Keywords

  • Asymptotic behavior
  • bi-stability
  • logistic behavior
  • population dynamics
  • reduced reproduction
  • two-sex models

ASJC Scopus subject areas

  • Demography
  • Geography, Planning and Development
  • Agricultural and Biological Sciences(all)

Cite this

Reduced fertility and asymptotics of the logistic model. / Maxin, Daniel; Milner, Fabio Augusto; Sega, Laurentiu M.

In: Mathematical Population Studies, Vol. 23, No. 1, 02.01.2016, p. 37-49.

Research output: Contribution to journalArticle

Maxin, Daniel ; Milner, Fabio Augusto ; Sega, Laurentiu M. / Reduced fertility and asymptotics of the logistic model. In: Mathematical Population Studies. 2016 ; Vol. 23, No. 1. pp. 37-49.
@article{78f49589f11540eda3ea4327f22edb7a,
title = "Reduced fertility and asymptotics of the logistic model",
abstract = "This logistic model includes three age groups. Juveniles do not reproduce, and old individuals reproduce at a lower rate. Pairings between individuals of different fertility rates may lead to multiple equilibria and bi-stability: the total population converges to different limits depending on its initial size. The behavior is correlated with transition rates from high to low fertility groups and with the frequency of pairing among the various groups of reproduction level. The proportions of adults at equilibrium are roots of a quartic polynomial, alternating sinks and saddles. Necessary and sufficient conditions for the existence of bi-stability are provided for a simplified model.",
keywords = "Asymptotic behavior, bi-stability, logistic behavior, population dynamics, reduced reproduction, two-sex models",
author = "Daniel Maxin and Milner, {Fabio Augusto} and Sega, {Laurentiu M}",
year = "2016",
month = "1",
day = "2",
doi = "10.1080/08898480.2016.1117270",
language = "English (US)",
volume = "23",
pages = "37--49",
journal = "Mathematical Population Studies",
issn = "0889-8480",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

TY - JOUR

T1 - Reduced fertility and asymptotics of the logistic model

AU - Maxin, Daniel

AU - Milner, Fabio Augusto

AU - Sega, Laurentiu M

PY - 2016/1/2

Y1 - 2016/1/2

N2 - This logistic model includes three age groups. Juveniles do not reproduce, and old individuals reproduce at a lower rate. Pairings between individuals of different fertility rates may lead to multiple equilibria and bi-stability: the total population converges to different limits depending on its initial size. The behavior is correlated with transition rates from high to low fertility groups and with the frequency of pairing among the various groups of reproduction level. The proportions of adults at equilibrium are roots of a quartic polynomial, alternating sinks and saddles. Necessary and sufficient conditions for the existence of bi-stability are provided for a simplified model.

AB - This logistic model includes three age groups. Juveniles do not reproduce, and old individuals reproduce at a lower rate. Pairings between individuals of different fertility rates may lead to multiple equilibria and bi-stability: the total population converges to different limits depending on its initial size. The behavior is correlated with transition rates from high to low fertility groups and with the frequency of pairing among the various groups of reproduction level. The proportions of adults at equilibrium are roots of a quartic polynomial, alternating sinks and saddles. Necessary and sufficient conditions for the existence of bi-stability are provided for a simplified model.

KW - Asymptotic behavior

KW - bi-stability

KW - logistic behavior

KW - population dynamics

KW - reduced reproduction

KW - two-sex models

UR - http://www.scopus.com/inward/record.url?scp=84960344004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960344004&partnerID=8YFLogxK

U2 - 10.1080/08898480.2016.1117270

DO - 10.1080/08898480.2016.1117270

M3 - Article

VL - 23

SP - 37

EP - 49

JO - Mathematical Population Studies

JF - Mathematical Population Studies

SN - 0889-8480

IS - 1

ER -