Benditkis D. Investigation of critical cases of stability of nonlinear systems with quadratic right-hand side and models with weak delay

Investigation of critical cases of stability of nonlinear systems with quadratic right-hand side and models with weak delay. In this thesis there have been considered differential equation systems with quadratic right-hand side in critical cases of one and a pair of pure imaginary eigenvalues of linear part. Constructive stability conditions and stability region estimations have been obtained. Lyapunov function of quadratic form was being used during the investigation. There have been introduced a concept "systems with weak delay". It means linear systems, which have finite number of eigenvalues. Necessary and sufficient conditions of "weak delay " have been obtained. Solution of Cauchy problem have been written for general form of weak delay systems on the plane. Solution of Cauchy problem have been written for weak delay systems of triangle form in three-dimensional space. Stability conditions for the plane have been obtained. Mathematical model of interaction of nodes in computer network either withand without feedback was investigated. Two forms of linearization was carried out and Cauchy problem solution was written. Estimation of external disturbances and initial conditions influence was obtained.