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Dynamics of the diffusive Nicholson's blowflies equation with distributed delay

Published online by Cambridge University Press:  11 July 2007

S. A. Gourley  and
S. Ruan
S. A. Gourley
Affiliation:
Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 5XH, UK ([email protected])
S. Ruan
Affiliation:
Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 ([email protected])
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Abstract

In this paper we study the diffusive Nicholson's blowflies equation. Generalizing previous works, we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible. The linearized stability of the non-zero uniform steady state is studied in detail, mainly by using the principle of the argument. Global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations. Finally, we consider what bifurcations are possible from the non-zero uniform state in the case when it is unstable.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 6 , December 2000 , pp. 1275 - 1291
Copyright
Copyright © Royal Society of Edinburgh 2000

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