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