On the birth and death of algebraic limit cycles in quadratic differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Oliveira, Regilene (Universidade de São Paulo. Instituto de Ciências Matemáticas e Computação. Departamento de Matemática (Brazil))
Zhao, Yulin (Sun Yat-sen University. School of Mathematics (People's Republic of China))

Date:	2021
Abstract:	In 1958 started the study of the families of algebraic limit cycles in the class of planar quadratic polynomial differential systems. In the present we known one family of algebraic limit cycles of degree 2 and four families of algebraic limit cycles of degree 4, and that there are no limit cycles of degree 3. All the families of algebraic limit cycles of degree 2 and 4 are known, this is not the case for the families of degree higher than 4. We also know that there exist two families of algebraic limit cycles of degree 5 and one family of degree 6, but we do not know if these families are all the families of degree 5 and 6. Until today it is an open problem to know if there are algebraic limit cycles of degree higher than 6 inside the class of quadratic polynomial differential systems. Here we investigate the birth and death of all the known families of algebraic limit cycles of quadratic polynomial differential systems.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017SGR1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycles ; Hopf bifurcation ; Homoclinic orbits ; Heteroclinic orbits ; Quadratic polynomial differential systems
Published in:	European Journal of Applied Mathematics, Vol. 32, Issue 2 (April 2021) , p. 317-336, ISSN 0956-7925

DOI: 10.1017/S0956792520000145

Postprint 22 p, 833.4 KB

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