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Zbl 0935.34035
Hsu, Sze-Bi; Hwang, Tzy-Wei
Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type. (English)
[J] Taiwanese J. Math. 3, No.1, 35-53 (1999). ISSN 1027-5487

The authors study the Hopf bifurcation for the Holling-Tanner predator-prey model. Using Andronov-Hopf bifurcation theorem, they show that for some parameters the bifurcation is subcritical, i.e., there exists a small-amplitude repelling periodic orbit enclosing a stable equilibrium and separating it from another, stable limit cycle. The paper also summarizes earlier results of {\it S.-B. Hsu} and {\it T.-W. Hwang} [SIAM J. Appl. Math. 55, 763-783 (1995; Zbl 0832.34035)] on global asymptotical stability of the internal equilibrium.
[David S.Boukal (České Budějovice)]

MSC 2000:: *34C23 Bifurcation (periodic solutions)
37G15 Bifurcations of limit cycles and periodic orbits
92D25 Population dynamics
34C05 Qualitative theory of some special solutions of ODE
34D23 Global stability

Keywords: Holling-Tanner model; predator-prey system; Andronov-Hopf bifurcation; multiple limit cycle

Citations: Zbl 0832.34035

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