Ratio-dependent predator-prey models set up a challenging issue regarding their dynamics near the origin. This is due to the fact that such models are undefined at (0,0). We study the analytical behavior at (0,0) for a common ratio-dependent model and demonstrate that this equilibrium can be either a saddle point or an attractor for certain trajectories. This fact has important implications concerning the global behavior of the model, for example regarding the existence of stable limit cycles.
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