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Stability and Hopf bifurcation analysis for Nicholson's blowflies equation with non-local delay†

Published online by Cambridge University Press:  10 August 2012

RUI HU  and
YUAN YUAN
RUI HU
Affiliation:
Department of Mathematical and Statistical Sciences, University of AlbertaEdmonton AB T6G 2G1Canada email: (rhu@ualberta.ca)
YUAN YUAN
Affiliation:
Department of Mathematics and Statistics, Memorial University of NewfoundlandSt. John's NL A1C 5S7Canada
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Abstract

We consider a diffusive Nicholson's blowflies equation with non-local delay and study the stability of the uniform steady states and the possible Hopf bifurcation. By using the upper- and lower solutions method, the global stability of constant steady states is obtained. We also discuss the local stability via analysis of the characteristic equation. Moreover, for a special kernel, the occurrence of Hopf bifurcation near the steady state solution and the stability of bifurcated periodic solutions are given via the centre manifold theory. Based on laboratory data and our theoretical results, we address the influence of various types of vaccinations in controlling the outbreak of blowflies.

Keywords

Nicholson's blowflies equationDiffusionNon-local delayHopf bifurcationHomogeneous Neumann boundary condition

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 6 , December 2012 , pp. 777 - 796
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

†

Project supported in part by Natural Science and Engineering Research Council of Canada.

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