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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Received: 16 April 1999 / Revised version: 4 October 1999 /¶Published online: 5 May 2000
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Schley, D., Gourley, S. Linear stability criteria for population models with periodically perturbed delays. J Math Biol 40, 500–524 (2000). https://doi.org/10.1007/s002850000034
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DOI: https://doi.org/10.1007/s002850000034