Stability of a delay equation arising from ajuvenile-adult model

Azmy S. Ackleh; Keng Deng

doi:10.3934/mbe.2010.7.729

Article Contents

2010, Volume 7, Issue 4: 729-737. Doi: 10.3934/mbe.2010.7.729

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Stability of a delay equation arising from a juvenile-adult model

Azmy S. Ackleh^1, and
Keng Deng^1,

1.
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010

Received: April 30, 2010

Revised: June 30, 2010

Published: September 2010

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Abstract

We consider a delay equation that has been formulated from a juvenile-adult population model. We give respective conditions on the vital rates to ensure local stability of the positive equilibrium and global stability of the trivial equilibrium. We also show that under certain conditions the equation undergoes a Hopf bifurcation. We then study global asymptotic stability and present bifurcation diagrams for two special cases of the model.

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Mathematics Subject Classification: Primary: 34A34, 34D20, 92D25.

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