Abstract
The phase portraits, existence and uniqueness of stable limit cycles and Hopf bifurcations of the well-known Holling–Tanner models for predator–prey interactions are studied. The ranges of the parameters involved are provided under which the unique interior equilibrium can be determined to be a stable (or an unstable) node or focus. The Hopf bifurcations and the existence and uniqueness of stable limit cycles of the models are obtained by computing the Lyapunov number involved. Our results confirm some previous results observed and suggested from the real ecological systems.
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