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Mathematical Biosciences and Engineering

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

  • 1.
    Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010
  • Received: 01 May 2010 Accepted: 29 June 2018 Published: 01 October 2010

  • MSC : Primary: 34A34, 34D20, 92D25.

  • 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

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  • 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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  • © 2010 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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