Mathematical Biosciences and Engineering, 2010, 7(4): 729-737. doi: 10.3934/mbe.2010.7.729.

Primary: 34A34, 34D20, 92D25.

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

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

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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Keywords instability.; continuous juvenile-adult model; stability; Delay equation

Citation: Azmy S. Ackleh, Keng Deng. Stability of a delay equation arising from a juvenile-adult model. Mathematical Biosciences and Engineering, 2010, 7(4): 729-737. doi: 10.3934/mbe.2010.7.729


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