In each case, two uncoupled related subsystems are constructed and analyzed. It is shown that appropriate properties of the subsystems will insure that the full system has a steady-state solution which is strictly positive in each component. The problem is applicable to the study of the coexistence of all species when two subgroups of species are mixed together. The method of bifurcation and upper-lower solutions are used in the analysis.
Bifurcation theory is used in the construction of lower solutions.