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Zbl 1183.92085
Sun, Xiao-Ke; Huo, Hai-Feng; Xiang, Hong
Bifurcation and stability analysis in predator-prey model with a stage-structure for predator. (English)
[J] Nonlinear Dyn. 58, No. 3, 497-513 (2009). ISSN 0924-090X; ISSN 1573-269X/e

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 2000:: *92D40 Ecology
34C60 Applications of qualitative theory of ODE
34C23 Bifurcation (periodic solutions)
65C20 Models (numerical methods)

Keywords: Hopf bifurcation; time delay

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Zentralblatt MATH Berlin [Germany]