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Zbl 1205.34089
Song, Yongli; Yuan, Sanling; Zhang, Jianming
Bifurcation analysis in the delayed Leslie-Gower predator-prey system. (English)
[J] Appl. Math. Modelling 33, No. 11, 4049-4061 (2009). ISSN 0307-904X

Summary: The delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can occur as the delay crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of {\it J. Wu} [Trans. Am. Math. Soc. 350, No.~12, 4799--4838 (1998; Zbl 0905.34034)] for functional differential equations, we may show the global existence of periodic solutions.

MSC 2000:: *34K18 Bifurcation theory of functional differential equations
92D25 Population dynamics
34K60 Applications of functional-differential equations

Keywords: predator-prey system; delay; stability; Hopf bifurcation; periodic solution

Citations: Zbl 0905.34034

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