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

Belattar, Meryem and Cheurfa, Rachid and Bendjeddou, Ahmed and Santana, Paulo (2023) A class of nonlinear oscillators with non-autonomous first integrals and algebraic limit cycles. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (50). pp. 1-13. ISSN 1417-3875

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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.

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