On a model of the predator-prey system with delay

We study the dynamics of the size of an isolated population with delay in the birth rate, and the corresponding predator-prey system. For the prey population, it is assumed that only those individuals who were alive at a certain prior time can reproduce; more precisely, only those who are still alive at the present moment can reproduce. We study the general properties of the models and their dynamic regimes. In particular, we show that the form of delay proposed does not lead to instability of nontrivial equilibrium states.