Abstract: A ratio dependent predator-prey system with Holling type III functional response is considered. A sufficient condition of the global asymptotic stability for the positive equilibrium and existence of the limit cycle are given by studying locally asymptotic stability of the positive equilibrium. The condition under which positive equilibrium is not a hyperbolic equilibrium is investigated using Hopf bifurcation.

Key words: Hopf bifurcation, ratio-dependent, global asymptotic stability, functional response