An alternative formulation for a delayed logistic equation

After a brief review of the history and dynamics of the classical logistic and delayed logistic equation models, an alternative expression for a delayed logistic equation is derived assuming that the rate of change of the population depends on three components: growth, death, and intraspecific competition, with the delay in the growth component. In our formulation, we incorporate the delay in the growth term in a manner consistent with the rate of instantaneous decline in the population given by the model. A complete global analysis shows that unlike the dynamics of the classical logistic delay differential equation model,no sustained oscillations are possible. Instead, the dynamics of this model are more reminiscent of the classical logistic ordinary differential equations growth model, but with some important differences. Implications for incorporating delays in population models are considered.