Permanence criteria for general delayed discrete nonautonomous nn-species Kolmogorov systems and its applications

In this paper, the permanence for the general nonautonomous nn-species discrete Kolmogorov systems with delays is studied. By using the method of multiple discrete Lyapunov-like functionals, a quite general sufficient condition is established. As application of this result, new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure-delayed nn-species Lotka–Volterra competitive systems and food chain systems. Particularly, as special cases, a series of new sufficient conditions on the permanence for the discrete nonautonomous pure-delayed Lotka–Volterra two-species competitive systems, predator–prey systems and three-species food chain systems, and the discrete autonomous pure-delayed Lotka–Volterra competition systems and food chain systems are obtained.