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GLOBAL DYNAMICS OF THE MAY-LEONARD SYSTEM WITH A DARBOUX INVARIANT

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Autor(es):
Oliveira, Regilene ; Valls, Claudia
Número total de Autores: 2
Tipo de documento: Artigo Científico
Fonte: Electronic Journal of Differential Equations; v. N/A, p. 19-pg., 2020-06-03.
Resumo

We study the global dynamics of the classic May-Leonard model in R-3. Such model depends on two real parameters and its global dynamics is known when the system is completely integrable. Using the Poincare compactification on R-3 we obtain the global dynamics of the classical May-Leonard differential system in R-3 when beta = -1 - alpha. In this case, the system is non-integrable and it admits a Darboux invariant. We provide the global phase portrait in each octant and in the Poincare ball, that is, the compactification of R-3 in the sphere S-2 at infinity. We also describe the omega-limit and alpha-limit of each of the orbits. For some values of the parameter alpha we find a separatrix cycle F formed by orbits connecting the finite singular points on the boundary of the first octant and every orbit on this octant has F as the omega-limit. The same holds for the sixth and eighth octants. (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
Processo FAPESP: 19/21181-0 - Novas fronteiras na Teoria de Singularidades
Beneficiário:Regilene Delazari dos Santos Oliveira
Modalidade de apoio: Auxílio à Pesquisa - Temático