Fedorova

One method of the qualitative analysis of a dynamical system is to estimate the position of its compact invariant sets closely associated with bounded trajectories of the system. As a solution to such a problem, one can use a localizing set, i.e. a set in the phase space containing all invariant compact sets of the system. In this article two continuous two-dimensional dynamical systems describing behavior of some biological systems are explored. For each of these systems a family of localizing sets is constructed, and then the intersection of the family is calculated. For the first system the solution was obtained analytically and for the second one the numerical procedure of constructing localizing sets was proposed. The investigation results are shown in figures.