Family of finite-dimensional maps induced by a logistic equation with a delay

This article discusses a family of maps that are used in the numerical simulation of a logistic equation with delay. This equation is widely used in problems of mathematical ecology. At the same time, the presented maps themselves can serve as models of the dynamics of populations; therefore, their study is of considerable interest. The paper compares the properties of the trajectories of these mappings and the original equation with delay. It is shown that the behavior of the solutions of maps can be quite complicated, while the logistic equation with delay has only a stable equilibrium state or cycle.