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JOURNALS // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Archive

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019 Number 3, Pages 65–74 (Mi basm537)

Research articles

Polynomial differential systems with explicit expression for limit cycles

Mouna Yahiaoui, Rachid Boukoucha

Lab. de Mathématiques Appliquées, Université de Bejaia, 06000 Bejaia, Algérie

Abstract: In this paper we give an explicit expression of invariant algebraic curves of 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.

Keywords and phrases: limit cycle, Riccati equation, invariant algebraic curve, first integral.

MSC: 34C05, 34C07, 37C27, 37K10

Received: 13.04.2019

Language: English



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