Global phase portraits of Kukles differential systems with homogenous polynomial nonlinearities of degree 5 having a center and their small limit cycles
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Silva, Mauricio Fronza da (Universidade Federal de Santa Maria(Brazil). Departamento de Matemática)

Date:	2016
Abstract:	We provide the nine topological global phase portraits in the Poincaré disk of the family of the centers of Kukles polynomial differential systems of the form x = -y, y= x ax^5y bx^3y^3 cxy^5, where x,y\R and a,b,c are real parameters satisfying a^2 b^2 c^2 0. Using averaging theory up to sixth order we determine the number of limit cycles which bifurcate from the origin when we perturb this system first inside the class of all homogeneous polynomial differential systems of degree 6, and second inside the class of all polynomial differential systems of degree 6.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Centers ; Kukles ; Phase portrait ; Poincaré disk ; Polynomial vector fields
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 26 Núm. 3 (2016) , p. 1650044 (25 pages), ISSN 1793-6551

DOI: 10.1142/S0218127416500449

Postprint 25 p, 3.2 MB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles