Periodic solutions of a discrete time stage-structure model

In this paper, we investigate the following discrete periodic stage-structure model with diffusion: I1(k+1)=I1(k)exp-b(k)-c(k)+a(k)M1(k)I1(k),M1(k+1)=M1(k)exp-D12(k)-α(k)M1(k)+D12(k)M2(k)+c(k)I1(k)M1(k),M2(k+1)=M2(k)exp-D21(k)-β(k)+D21(k)M1(k)M2(k).The sufficient and realistic conditions are obtained for the existence of positive periodic solutions of this system.