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

Consider the following discrete models of nonautonomous Lotka–Volterra type:   Ni(p + 1) = Ni(p) exp ci(p)− ai(p)Ni(p) − n j=1 m l=0 al ij (p)Nj (p − kl) , 1 i n, p = 0, 1, 2, . . . , Ni(p) = Nip 0, p 0, and Ni0 > 0, 1 i n, where each ci(p), ai(p) and al ij (p) are bounded for p 0 and   infp 0 ai(p) > 0, a0 ii(p) ≡ 0, 1 i n, al ij (p) 0, 1 i j n, 0 l m, k0 = 0, integers kl 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.  2002 Elsevier Science (USA). All rights reserved.