On the properties of systems of differential equations and problems of optimal resource extraction

A classification of autonomous nonlinear systems of ordinary differential equations is proposed. The behavior of trajectories of systems of each class is described and it is shown that solutions of systems of the first and second classes have the property of monotony of solutions relative to initial data. One of the variants of the compari-son theorem for these systems is given. Examples of systems of the second and third classes for models of interaction between two biological species are consid-ered. It is shown that for systems of different classes, the problems of optimal ex-traction of a renewable resource are solved in different ways; in particular, the ques-tion of the expediency of extracting one type of resource or two types is discussed.