Abstract: This paper is denoted to the qualitative analysis of two species predator-prey model with Boiling’s type III functional response. Conditions for the global stability ofnontrivial equilibrium points and conditions for the existence and uniqueness of limit cycles around the positive equilibrium point are obtained. The biological interpretations of these conditions are discussed. The authors believe that the conditions established in this paper are new to literature.

Key words: unbalance elastic rotor, safety margin, comparative positive-area criterion (CPAC), bifurcation and chaos