Extinction in a nonautonomous competitive Lotka–Volterra system

A nonautonomous competitive Lotka–Volterra system is considered in this work. Sufficient conditions on the coefficients are given to guarantee that all but one of the species are driven to extinction. It is shown that these conditions are weaker than those of Montes de Oca and Zeeman [F. Montes de Oca, M.L. Zeeman, Extinction in nonautonomous competitive Lotka–Volterra systems, Proc. Amer. Math. Soc. 124 (1996) 3677–3687].