Family of differential systems with explicit algebraic and non-algebraic limit cycles

Abstract

In this memory, we present some fundamental notions of the qualitative theory of differential equations, precisely on nonlinear polynomial planar differential equation systems which aim to find the properties of their solutions (such as equilibrium points, invariant curves, and periodic solutions).We give details about the research of A.Gasull, H.Gizcomini, J.Torregrosa. In the article entitled: "Explicit non-algebraic limit cycles for polynomial systems" published by: "Elsevier" on January 3, 2006.