Extinction of species in nonautonomous Lotka-Volterra systems

Abstract

A nonautonomous n n th order Lotka-Volterra system of differential equations is considered. It is shown that if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 n-1 components tend to zero, while the first one will stabilize at a certain solution of a logistic equation.