Applied Physics and Mathematics Annotation << Back ANALYSIS OF REGIONAL STABILITY OF DYNAMICAL SYSTEMS USING METHODS OF ALGEBRAIC GEOMETRY S.N. CHUKANOV, I.S. CHUKANOV The paper investigates the region of attraction (ROA) estimation for polynomial systems by numerically solving polynomial equations based on the homotopy continuation method. One of the problems in the theory of nonlinear systems is the problem of estimating the area of attraction of an equilibrium position, which is defined as a set of initial conditions that converge to equilibrium as time approaches infinity. Usually, the attraction domain is approximated by a set of sublevels of the Lyapunov function. If the time derivative of the Lyapunov function is negative definite in the set of sublevels, then the set of sublevels is contained in ROA. The paper describes a method for numerical calculation of the optimal set of sublevels for low-dimensional polynomial systems based on the homotopy continuation method. The paper considers finding the point of contact between the level set of the Lyapunov function V(x) and the surface of its time derivative using the technique of Gröbner bases. Keywords: equilibrium position of a polynomial system, domain of attraction, Lyapunov function, homotopy continuation method, Gröbner basis. DOI: 10.25791/pfim.03.2022.1231 Pp. 26-30.