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IMI/Publicaţii/BASM/Ediţii/BASM n.3(91), 2019/

Polynomial differential systems with explicit expression for limit cycles

Authors: Mouna Yahiaoui, Rachid Boukoucha

Abstract

In this paper we give an explicit expression of invariant algebraic curves of a multi-parameter planar polynomial differential systems of degree nine, then we prove that these systems are integrable and we introduce an explicit expression of a first integral. Moreover, we determine sufficient conditions for these systems to possess two limit cycles: one of them is algebraic and the other one is shown to be non-algebraic, explicitly given. Concrete examples exhibiting the applicability of our result are introduced.

Lab. de Mathèmatiques Appliquèes, Universitè de Bejaia,
06000 Bejaia, Algèrie
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