On a problem of control of the size of populations (Q677370)

Much research is devoted to problems of analysis of dynamics and control of sizes of populations of animals and microorganisms. A vast list of references on this subject is presented. Depending on conditions of existence of biological habitats under consideration, different mathematical models of the evolution type are used for description of processes of growth of populations. We consider the problem of optimal control of the size of a population for the case where the dynamics of a one-species population is described by a one-dimensional logistic model. For processes of infinite horizon, exact solutions are obtained for problems of synthesis of optimal control for two types of dynamic models: the ``usual'' logistic model and the logistic model with aftereffect.