| Full text | |
| Author(s): |
Oliveira, Regilene
;
Valls, Claudia
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Electronic Journal of Differential Equations; v. N/A, p. 19-pg., 2020-06-03. |
| Abstract | |
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) | |
| FAPESP's process: | 17/20854-5 - Qualitative theory of ordinary differential equations: integrability, periodic orbits and phase portraits |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/21181-0 - New frontiers in Singularity Theory |
| Grantee: | Regilene Delazari dos Santos Oliveira |
| Support Opportunities: | Research Projects - Thematic Grants |