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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 {\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.

##### MSC:
 34C23 Bifurcation (ODE) 37G15 Bifurcations of limit cycles and periodic orbits 92D25 Population dynamics (general) 34C05 Location of integral curves, singular points, limit cycles (ODE) 34D23 Global stability of ODE