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Global Hopf bifurcation in the Leslie-Gower predator-prey model with two delays. (English) Zbl 1238.34130
Summary: The Leslie-Gower predator-prey system with two delays is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation theorem for functional differential equations, we show the global existence of periodic solutions.
MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34K18Bifurcation theory of functional differential equations
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