In the present work the methods of computation of Lyapunov quantities and localization of
limit cycles are demonstrated. These methods are applied to investigation of quadratic …

The computation of Lyapunov quantities is closely connected with the important in
engineering mechanics question of dynamical system behavior near to boundary of the …

A direct method is proposed for studying the behavior of two-dimensional dynamical
systems in the critical case when the linear part of the system has two purely imaginary …

This paper provides a survey on symbolic computational approaches for the analysis of
qualitative behaviors of systems of ordinary differential equations, focusing on symbolic and …

One of the central problems in studying small cycles in the neighborhood of equilibrium
involves computation of Lyapunov's quantities. While Lyapunov's first and second quantities …

We propose a new hybrid symbolic-numerical approach to the center-focus problem. The
method allowed us to obtain center conditions for a three-dimensional system of differential …

Efficient methods in the search for the periodic oscillations of dynamical systems are
described. Their application to the sixteenth Hilbert problem for quadratic systems and the …

We demonstrate the utilization of the fundamental principle of nonlinear dynamics, namely,
the Liénard-type representations of ordinary differential equations, also referred to as fast …

COMPUTATION OF THE FIRST LYAPUNOV QUANTITY FOR SECOND-ORDER DYNAMICAL
SYSTEM 1 Leonov GA, Kuznetsov NV Page 1 COMPUTATION OF THE FIRST LYAPUNOV …

Описаны эффективные методы поиска периодических колебаний динамических
систем. Рассмотрено их применение к шестнадцатой проблеме Гильберта для …