An Exactly Solvable Planar Differential System Of Degree Six With An Explicit Algebraic Limit Cycle

Autor(es)

Belattar, Meryem ; Cheurfa, Rachid ; Bendjeddou, Ahmed ; Santana, Paulo

• Tipo de documento: Artigo Científico
• Fonte: APPLIED MATHEMATICS E-NOTES; v. 24, p. 12-pg., 2024-01-01.

Resumo

A multi-parameter and planar first-order autonomous differential system of degree six is shown to be integrable. More specifically, we show that it possesses a time-dependent first integral and an autonomous one. This enables us to analytically obtain the solutions. Moreover, under some appropriate conditions, we prove that this system admits an explicit hyperbolic algebraic limit cycle. Finally, we draw the possible phase portraits on the Poincare<acute accent> disk and illustrate the geometric behavior of the trajectories of the system. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 21/01799-9 - Estudo de campos de vetores com aplicações na teoria dos jogos
• Beneficiário: Paulo Henrique Reis Santana
• Modalidade de apoio: Bolsas no Brasil - Doutorado