Phase portraits of Abel quadratic differential systems of the second kind

ABSTRACT

We provide normal forms and the global phase portraits on the Poincaré disk of some Abel quadratic differential equations of the second kind. Moreover, we also provide the bifurcation diagrams for these global phase portraits.

KEYWORDS:

• Abel differential equation of the second kind
• Kukles differential system
• quadratic differential system
• phase portrait

2010 MATHEMATICS SUBJECT CLASSIFICATION CODES:

• 34A34
• 34C20
• 34C23
• 34C05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

A. Ferragut is supported by the MINECO grants [grant number MTM2016-77278-P], [grant number MTM2013-40998-P] and by the Universitat Jaume I grant [grant number P1-1B2015-16]. C. Valls is supported by Portuguese National Funds through FCT – Fundação para a Ciência e a Tecnologia [PTDC/MAT/117106/2010] and by CAMGSD.