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Linear stability criteria for population models with periodically perturbed delays

Linear stability criteria for population models with periodically perturbed delays
Linear stability criteria for population models with periodically perturbed delays
We examine some simple population models that incorporate a time delay which is not a constant but is instead a known periodic function of time. We examine what effect this periodic variation has on the linear stability of the equilibrium states of scalar population models and of a simple predator prey system. The case when the delay differs from a constant by a small amplitude periodic perturbation can be treated analytically by using two-timing methods. Of particular interest is the case when the system is initially marginally stable. The introduction of variation in the delay can then have either a stabilising effect or a destabilising one, depending on the frequency of the periodic perturbation. The case when the periodic perturbation has large amplitude is studied numerically. If the fluctuation is large enough the effect can be stabilising.
scalar discrete delay models, logistic equation, predator-prey, variable time-delay, two-timing expansions
0303-6812
500-524
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Gourley, S.A.
1aa9c89e-dfca-43f6-ad4d-4ecbe379094c

Schley, D. and Gourley, S.A. (2000) Linear stability criteria for population models with periodically perturbed delays. Journal of Mathematical Biology, 40 (6), 500-524. (doi:10.1007/s002850000034).

Record type: Article

Abstract

We examine some simple population models that incorporate a time delay which is not a constant but is instead a known periodic function of time. We examine what effect this periodic variation has on the linear stability of the equilibrium states of scalar population models and of a simple predator prey system. The case when the delay differs from a constant by a small amplitude periodic perturbation can be treated analytically by using two-timing methods. Of particular interest is the case when the system is initially marginally stable. The introduction of variation in the delay can then have either a stabilising effect or a destabilising one, depending on the frequency of the periodic perturbation. The case when the periodic perturbation has large amplitude is studied numerically. If the fluctuation is large enough the effect can be stabilising.

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Published date: 2000
Keywords: scalar discrete delay models, logistic equation, predator-prey, variable time-delay, two-timing expansions

Identifiers

Local EPrints ID: 29282
URI: http://eprints.soton.ac.uk/id/eprint/29282
ISSN: 0303-6812
PURE UUID: 2789b461-71c0-4a4d-8900-ee4604986a4d

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Date deposited: 18 Jul 2006
Last modified: 08 Jan 2022 03:51

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Contributors

Author: D. Schley
Author: S.A. Gourley

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