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Approximating the Stability Region for a Differential Equation with a Distributed Delay

S. A. Campbell, R. Jessop (2009)

Mathematical Modelling of Natural Phenomena

We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a distribution independent stability region may be obtained in a similar way that delay independent...

Stability switches for some class of delayed population models

Joanna Skonieczna, Urszula Foryś (2011)

Applicationes Mathematicae

We study stability switches for some class of delay differential equations with one discrete delay. We describe and use a simple method of checking the change of stability which originally comes from the paper of Cook and Driessche (1986). We explain this method on the examples of three types of prey-predator models with delay and compare the dynamics of these models under increasing delay.

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