On the autonomous systems on a plane and limit cycles

Abstract

In the given article we have considered questions of the stability of continuous and smooth solutions of autonomous systems and of systems of first order differential equations in a general form in the first approximation. Analysis of stability is directly connected with the definition of the conditions of equilibrium and with the finding of stability of limit cycles. In this article also the asymptotic stability of periodical solution of system depending on the values of multipliers is explored. The example and mixed case are considered.