Average conditions for extinction in nonautonomous Kolmogorov systems

In this paper we consider nonautonomous competitive Kolmogorov systems, which constitute a generalization of the classical Lotka–Volterra competition model. Applying Ahmad and Lazer’s definitions of lower and upper averages of a function, we give the average conditions which guarantee that rr of the NN species are permanent while the remaining N−rN−r are driven to extinction.