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

Pages: 729 - 737, Volume 7, Issue 4, October 2010

doi:10.3934/mbe.2010.7.729       Abstract        References        Full Text (251.2K)       Related Articles

Azmy S. Ackleh - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, United States (email)
Keng Deng - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010, United States (email)

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.

Keywords:  Delay equation, continuous juvenile-adult model, stability, instability.
Mathematics Subject Classification:  Primary: 34A34, 34D20, 92D25.

Received: May 2010;      Accepted: July 2010;      Published: October 2010.

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