Open AccessDiscrete or distributed delay? Effects on stability of population growth
Author(s) -
Edoardo Beretta,
Dimitri Breda
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016.13.19
Subject(s) - stability (learning theory) , control theory (sociology) , mathematics , delay differential equation , variance (accounting) , population , domain (mathematical analysis) , computer science , mathematical analysis , differential equation , economics , demography , control (management) , accounting , artificial intelligence , machine learning , sociology
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.