The existence of positive periodic solutions for a delayed
discrete predator-prey model with Holling-type-III functional
response N1(k+1)=N1(k)exp{b1(k)−a1(k)N1(k−[τ1])−α1(k)N1(k)N2(k)/(N12(k)+m2N22(k))}, N2(k+1)=N2(k)exp{−b2(k)+α2(k)N12(k−[τ2])/(N12(k−[τ2])+m2N22(k−[τ2]))} is established by using the coincidence
degree theory. We also present sufficient conditions for the
globally asymptotical stability of this system when all the delays
are zero. Our investigation gives an affirmative exemplum for the
claim that the ratio-dependent predator-prey theory is more
reasonable than the traditional prey-dependent predator-prey
theory.