Periodic solutions and stability for a delayed discrete ratio-dependent predator-prey system with Holling-type functional response

摘要

The existence of positive periodic solutions for a delayeddiscrete predator-prey model with Holling-type-III functionalresponseN1(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 coincidencedegree theory. We also present sufficient conditions for theglobally asymptotical stability of this system when all the delaysare zero. Our investigation gives an affirmative exemplum for theclaim that the ratio-dependent predator-prey theory is morereasonable than the traditional prey-dependent predator-preytheory.