Multicomponent Gause principle in models of biological communities
Dorodnicyn Computing Center, RAS
119333 Moscow, Vavilova, 40
e-mail: razzh@mail.ru
Refined formulation of Gause competition exclusion principle is proposed that guaranties vanishing at least one species in a community with more species than the number of available resources. Developed is a theory of achieving infinitely small values by more than one component within the framework of an ODE system that serves to model the dynamics of a biological community with n species. It is proved that, in the robust case, the total number of such components is equal to at least n—m whenever the Malthusian vector-function is located on an m-dimensional hyperplane separated from the origin. The theory is also applied to Volterra-type system that has the Malthusian function that depends linearly on m independent resources.
