Quadratic system of two differential equations with six limit cycles: two approaches to problem analysis

Abstract

In this paper, we propose two approaches to analyze the dynamic properties of a system of two differential equations with quadratic nonlinearity. It was demonstrated that both the method known from the literature and the method proposed by the authors of this paper give the same result; namely, in such nonlinear dynamic systems there are two foci and six limit cycles in the 3:3 arrangement.