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Hopf bifurcation in a three-species system with delays. (English) Zbl 1209.92058
Summary: A kind of three-species system with Holling II functional response and two delays is introduced. Its local stability and the existence of Hopf bifurcation are demonstrated by analyzing the associated characteristic equation. By using the normal form method and center manifold theorem, explicit formulas to determine the direction of the Hopf bifurcation and the stability of bifurcating periodic solution are also obtained. In addition, the global existence results of periodic solutions bifurcating from Hopf bifurcations are established by using a global Hopf bifurcation result. Numerical simulation results are also given to support our theoretical predictions.
MSC:
92D40Ecology
34K18Bifurcation theory of functional differential equations
34K13Periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
65C60Computational problems in statistics
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