Oscillations in age-structured population models with an Allee effect

J. M. Cushing

doi:10.1016/0377-0427(94)90349-2

Oscillations in age-structured population models with an Allee effect

J. M. Cushing

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

A nonautonomous ordinary differential delay equation for the birth rate of a model age-structured population is derived under the assumptions that nonlinear density effects on fertility exhibit an "Allee effect". It is shown how this assumption produces an interval of inherent net reproductive numbers less than one on which there exist two stable (asymptotic) equilibria. Furthermore, in the presence of a maturation delay and a sufficiently narrow age-specific fertility window, numerical solutions show that a certain type of attracting, large amplitude "synchronous" oscillation can also exist on this interval. A heuristic argument is given for the existence of such oscillations using the model obtained when the length of the fertility window shrinks to zero.

Original language	English (US)
Pages (from-to)	71-80
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	52
Issue number	1-3
DOIs	https://doi.org/10.1016/0377-0427(94)90349-2
State	Published - Jul 20 1994

Keywords

Allee effect
Delay differential equations
Maturation delays
Synchronous oscillations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/0377-0427(94)90349-2

Cite this

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title = "Oscillations in age-structured population models with an Allee effect",

abstract = "A nonautonomous ordinary differential delay equation for the birth rate of a model age-structured population is derived under the assumptions that nonlinear density effects on fertility exhibit an {"}Allee effect{"}. It is shown how this assumption produces an interval of inherent net reproductive numbers less than one on which there exist two stable (asymptotic) equilibria. Furthermore, in the presence of a maturation delay and a sufficiently narrow age-specific fertility window, numerical solutions show that a certain type of attracting, large amplitude {"}synchronous{"} oscillation can also exist on this interval. A heuristic argument is given for the existence of such oscillations using the model obtained when the length of the fertility window shrinks to zero.",

keywords = "Allee effect, Delay differential equations, Maturation delays, Synchronous oscillations",

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Y1 - 1994/7/20

N2 - A nonautonomous ordinary differential delay equation for the birth rate of a model age-structured population is derived under the assumptions that nonlinear density effects on fertility exhibit an "Allee effect". It is shown how this assumption produces an interval of inherent net reproductive numbers less than one on which there exist two stable (asymptotic) equilibria. Furthermore, in the presence of a maturation delay and a sufficiently narrow age-specific fertility window, numerical solutions show that a certain type of attracting, large amplitude "synchronous" oscillation can also exist on this interval. A heuristic argument is given for the existence of such oscillations using the model obtained when the length of the fertility window shrinks to zero.

AB - A nonautonomous ordinary differential delay equation for the birth rate of a model age-structured population is derived under the assumptions that nonlinear density effects on fertility exhibit an "Allee effect". It is shown how this assumption produces an interval of inherent net reproductive numbers less than one on which there exist two stable (asymptotic) equilibria. Furthermore, in the presence of a maturation delay and a sufficiently narrow age-specific fertility window, numerical solutions show that a certain type of attracting, large amplitude "synchronous" oscillation can also exist on this interval. A heuristic argument is given for the existence of such oscillations using the model obtained when the length of the fertility window shrinks to zero.

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KW - Delay differential equations

KW - Maturation delays

KW - Synchronous oscillations

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Oscillations in age-structured population models with an Allee effect

Abstract

Keywords

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