Discrete or distributed delay? Effects on stability of population growth

The growth of a population subject to maturation delay is modeled by using either a discrete delay or a delay continuously distributed over the population. The occurrence of stability switches (stable-unstable-stable) of the positive equilibrium as the delay increases is investigated in both cases....

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Bibliographic Details
Published inMathematical biosciences and engineering : MBE Vol. 13; no. 1; pp. 19 - 41
Main Authors Beretta, Edoardo, Breda, Dimitri
Format Journal Article
LanguageEnglish
Published United States AIMS Press 01.02.2016
Subjects
Animals
Birth Rate
Computer Simulation
delta$-dirac distribution
gamma distribution
Humans
local asymptotic stability analysis
maturation delay
Models, Statistical
Mortality
Population Growth
stability switches
Survival Rate
Time Factors
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Summary:The growth of a population subject to maturation delay is modeled by using either a discrete delay or a delay continuously distributed over the population. The occurrence of stability switches (stable-unstable-stable) of the positive equilibrium as the delay increases is investigated in both cases. Necessary and sufficient conditions are provided by analyzing the relevant characteristic equations. It is shown that for any choice of parameter values for which the discrete delay model presents stability switches there exists a maximum delay variance beyond which no switch occurs for the continuous delay model: the delay variance has a stabilizing effect. Moreover, it is illustrated how, in the presence of switches, the unstable delay domain is as larger as lower is the ratio between the juveniles and the adults mortality rates.
ISSN:1551-0018
DOI:10.3934/mbe.2016.13.19