Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point-Reference-Cited by-同舟云学术

Two Non Algebraic Limit Cycles of a Class of Polynomial Differential Systems with Non-Elementary Equilibrium Point

Published:2021-12-01 Issue:2 Volume:79 Page:33-46
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Benadouane Sabah¹,Berbache Aziza²,Bendjeddou Ahmed¹

Affiliation:

1. 1 Department of Mathematics, University Ferhat Abbas Sétif 1 , Sétif , ALGERIA

2. 2 Department of Mathematics , University of Bordj Bou Arréridj , Bordj Bou Arréridj , ALGERIA

Abstract

Abstract The problems of existence of limit cycles and their numbers are the most difficult problems in the dynamical planar systems. In this paper, we study the limit cycles for a family of polynomial differential systems of degree 6k + 1, k ∈ ℕ*, with the non-elementary singular point. Under some suitable conditions, we show our system exhibiting two non algebraic or two algebraic limit cycles explicitly given. To illustrate our results we present some examples.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0018

Reference16 articles.

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3. [3] BENDJEDDOU, A.—BERBACHE, A.: A class of differential system of odd degree with explicit non algebraic limit cycle, Int. Electron. J. Pure Appl. Math. 9 (2015), no. 4, 243–254.

4. [4] BENDJEDDOU, A.—CHEURFA, R.: Coexistence of algebraic and non-algebraic limit cycles for quintic Polynomial differential systems, Electron. J. Differential Equations 2017, Paper no. 71, 7 pp.

5. [5] BERBACHE, A.—BENDJEDDOU, A.: Three explicit non-algebraic limit cycles for a class of polynomial differential systems, Appl. Math. E-Notes 20 (2020), 158–166.

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