Global stability of n Dimensional Lotka Volterra sub systems

A set of sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium point in various sub models of the classic n dimensional Lotka Volterra system. The sub models are the following systems: competition chain system, competition modle between one and multi species,cooperative chain system,cooperative model between one and multi species. The criteria is in explicit forms of the parameters and thus is easily verifiable.