Bounding the domain of some three species food systems*

This paper presents results concerning the solution of the localization problem of any compact invariant set contained in the positive orthant for two 3-species food systems. The final localization domain in both of examples is a tetrahedron which may have linear excisions for some values of parameters. Some sufficient conditions of the nonexistence of compact invariant sets in the positive orthant are given as well. The results have been obtained by using the first order extremum conditions and the iteration theorem. Parameters of all localization sets are computed explicitly.