Stable steady state of some population models

Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=–x+D(x_t), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.