Siberian Federal University 
- Issue
- Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (4)
- Authors
- Belfar, Ahlam; Benterki, Rebiha
- Contact information
- Belfar, Ahlam: Department of Mathematics Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj El Anasser, Algeria; ; Benterki, Rebiha: Department of Mathematics Mohamed El Bachir El Ibrahimi University of Bordj Bou Arreridj El Anasser, Algeria;
- Keywords
- limit cycle; generalized Kukles differential system; averaging; method; phase portrait
- Abstract
In this work, we give the seven global phase portraits in the Poincar´e disc of the Kukles differential system given by x˙ = −y, y˙ = x + ax8 + bx4y4 + cy8, where x, y ∈ R and a, b, c ∈ R with a2 + b2 + c2 ̸= 0. Moreover, we perturb these system inside all classes of polynomials of eight degrees, then we use the averaging theory up sixth order to study the number of limit cycles which can bifurcate from the origin of coordinates of the Kukles differential system
- Pages
- 387–397
- DOI
- 10.17516/1997-1397-2020-13-4-387-397
- Paper at repository of SibFU
- https://elib.sfu-kras.ru/handle/2311/135355
Journal of Siberian Federal University. Mathematics & Physics / Centers and Limit Cycles of Generalized Kukles Polynomial Differential Systems: Phase Portraits and Limit Cycles
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