n the birth and death of algebraic limit cycles in quadratic differential system

Autor(es)

Llibre, Jaume ^[1] ; Oliveira, Regilene ^[2] ; Zhao, Yulin ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia - Spain

^[2] Univ Sao Paulo, Inst Ciencia Mat Comp, Dept Matemat, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[3] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong - Peoples R China

• Tipo de documento: Artigo Científico
• Fonte: EUROPEAN JOURNAL OF APPLIED MATHEMATICS; v. 32, n. 2, p. 317-336, APR 2021.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 17/20854-5 - Teoria qualitativa das equações diferenciais ordinárias: integrabilidade, órbitas periódicas e retratos de fase
• Beneficiário: Regilene Delazari dos Santos Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Regular