The authors consider a so-called ratio-dependent Holling-Tanner predator-prey model, where both components contain coefficients that depend on the ratio of predator and prey densities. By rescaling, the original six positive parameters are reduced to three, which are restricted in such a way that there exists a unique equilibrium
in the open positive quadrant. Generically,
is an attractor or repeller. In the first case, an extra condition on the parameters allows the construction of a Lyapunov function showing that
is globally attractive. If
is a repeller, the Poincaré-Bendixson theorem yields the existence of a limit cycle. Its uniqueness is, moreover, proved by transforming the given system into a Liénard system and using known results on the uniqueness of limit cycles for such systems.