Persistence and global stability for discrete models of nonautonomous Lotka–Volterra type

AbstractConsider the following discrete models of nonautonomous Lotka–Volterra type: Ni(p+1)=Ni(p)expci(p)−ai(p)Ni(p)−∑j=1n∑l=0maijl(p)Nj(p−kl),1⩽i⩽n,p=0,1,2,…,Ni(p)=Nip⩾0,p⩽0,andNi0>0,1⩽i⩽n, where each ci(p), ai(p) and aijl(p) are bounded for p⩾0 and infp⩾0ai(p)>0,aii0(p)≡0,1⩽i⩽n,aijl(p)⩾0,1⩽i⩽j⩽n,0⩽l⩽m,k0=0,integerskl⩾0,1⩽l⩽m. In this paper, to the above discrete system, we apply the techniques offered by Ahmad and Lazer (Nonlinear Anal. 40 (2000) 37–49), and establish similar conditions of the persistence and global asymptotic stability of the system