Open AccessStability of a delay equation arising from a juvenile-adult model
Author(s) -
Azmy S. Ackleh,
Keng Deng
Publication year - 2010
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2010.7.729
Subject(s) - hopf bifurcation , stability (learning theory) , mathematics , population model , exponential stability , juvenile , bifurcation , population , transcritical bifurcation , mathematical analysis , physics , nonlinear system , computer science , ecology , demography , biology , quantum mechanics , machine learning , sociology
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.