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Zbl 1238.34130
Ma, Yongfeng
Global Hopf bifurcation in the Leslie-Gower predator-prey model with two delays. (English)
[J] Nonlinear Anal., Real World Appl. 13, No. 1, 370-375 (2012). ISSN 1468-1218

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 2000:
*34K13 Periodic solutions of functional differential equations
92D25 Population dynamics
34K18 Bifurcation theory of functional differential equations

Keywords: Leslie-Gower model; global Hopf bifurcation

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