| Recently, some researchers studied the ratio-dependent predator-prey systems with Holling type II. In this paper, we study a ratio-dependent predator-Prey systems with Holling type III, the qualitative behavior of a class of ratio-dependent predator-Prey system at the origin in the interior of the first. quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist many kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and show the existence of eight qualitatively different types of system behaviors realized by various parameter values. Conditions of existence and non-existence of limit cycles and heteroclinic loop for the model are given. |
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