Multicomponent Gause's principle in models of biological communities

摘要

A generalization of the Gause competitive exclusion principle which guarantees the vanishing of at least one species in the community exceeding in number of species the number of available resources is presented. Theorems which guarantee the vanishing of a greater number of components under condition of the Malthusian vector function localizations in a set of smaller dimension are formulated. The theory developed here is applied to the case of Volterra type systems for which such vector functions are linear resource dependent and the number of resources is small.