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Stability and Hopf bifurcation analysis on a predator-prey model with discrete and distributed delays. (English) Zbl 1167.34382
Summary: A predator-prey model with discrete and distributed delays is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical value. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction and other properties of bifurcating periodic solutions are derived.
MSC:
34K20Stability theory of functional-differential equations
34C25Periodic solutions of ODE
34K18Bifurcation theory of functional differential equations
37G15Bifurcations of limit cycles and periodic orbits
92D25Population dynamics (general)