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Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure. (English) Zbl 1176.92056
Summary: A time-delay model for prey-predator growth with stage-structure is considered. At first, we investigate the stability and Hopf bifurcations by analyzing the distribution of the roots of the associated characteristic equation. Then, an explicit formula for determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations is derived, using normal form theory and center manifold arguments. Finally, some numerical simulations are carried out for supporting the analytic results.
MSC:
92D40Ecology
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations
65C20Models (numerical methods)
34K18Bifurcation theory of functional differential equations
References:
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