After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system. Although the corresponding results for the equilibrium E3 have been presented in a known literature, our results are more complete. The other is, what’s more important and difficult, to derive some sufficient conditions for the transcritical bifurcation and period-doubling bifurcation of this system at the equilibria E1, E2 and E3 to occur, which are completely new. Numerical simulations are performed to not only illustrate the theoretical results obtained but also find new dynamics – chaos occuring. Our results sufficiently display that this system is very sensitive to its parameters. Namely, the perturbations of different parameters in this system will produce different bifurcations.
MR(2000) Subject Classification: 39A28, 39A30.