Vanishing components in autonomous competitive Lotka-Volterra systems

Sufficient conditions are found for an n-dimensional autonomous competitive Lotka-Volterra system to have a component vanishing in an exponential rate as t -> infinity. These conditions incorporate a typical known result in the literature as a particular case. Moreover, if the n-dimensional system degenerates asymptotically to an m-dimensional subsystem as t -> infinity, then, under these conditions on the subsystem, the property that the ith component of every solution of the subsystem vanishes in an exponential rate is also preserved for the n-dimensional system. (C) 2009 Elsevier Inc. All rights reserved.