In this paper we investigate the existence of positive solutions to a system of differential equations which model a competitive system. Instead of assuming the usual logistic growth model for each population we allow the growth rate to increase for positive populations. This leads to models which exhibit the Allee effect.
"Positive solutions to a system of differential equations modeling a competitive interactive system with nonlogistic growth rates." Differential Integral Equations 10 (5) 929 - 945, 1997.