| Texto completo | |
| 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 |