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Bifurcation and stability analysis in predator-prey model with a stage-structure for predator. (English) Zbl 1183.92085
Summary: A predator-prey system with Holling type II functional response and stage-structure for the predator is presented. The stability and Hopf bifurcations of this model are studied by analyzing the associated characteristic transcendental equation. Further, an explicit formula for determining the stability and the direction of periodic solutions bifurcating from the positive equilibrium is derived by the normal form theory and center manifold arguments. Some numerical simulations are also given to illustrate our results.
MSC:
92D40Ecology
34C60Qualitative investigation and simulation of models (ODE)
34C23Bifurcation (ODE)
65C20Models (numerical methods)
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