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Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type. (English) Zbl 0935.34035
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 S.-B. Hsu and T.-W. Hwang [SIAM J. Appl. Math. 55, 763-783 (1995; Zbl 0832.34035)] on global asymptotical stability of the internal equilibrium.

MSC:
34C23 Bifurcation theory for ordinary differential equations
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
92D25 Population dynamics (general)
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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