A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles

Abstract

In this paper, we present a class of autonomous nonlinear oscillators with non-autonomous first integral. We prove explicitly the existence of a global sink which is, under some conditions, an algebraic limit cycle. For that class, we draw the possible phase portraits in the Poincaré disk.

Keywords

• algebraic limit cycles
• global sink
• non-autonomous first integrals