SUZANNE SUMNER
Two-dimensional pioneer-climax models of competing species differential equations are studied where the per capita growth rates are functions of weighted densities of the populations. The per capita growth rate of the pioneer species is monotonically decreasing whereas the per capita growth rate of the climax species is a one-humped function of the total weighted density. Constant rate forcing is introduced into the model representing stocking or harvesting. General formulas are calculated for determining the stability of the periodic orbit arising from a Hopf bifurcation.