Abstract
A stage-structured population model in a critical state is studied in this paper. By analyzing the corresponding characteristic equations, the local stability of the equilibria is discussed. Hopf bifurcations occurring at the positive equilibrium under some conditions are demonstrated. Taking time delay $$\tau $$ as bifurcating parameter, the direction and stability of Hopf bifurcation are carried out. The global continuation of periodic solutions bifurcating from the equilibrium is investigated. Finally, an example and numerical simulations are given.
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