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dc.contributor.authorOliveira, Regilene ( Orcid Icon 0000-0002-9628-5180 )
dc.contributor.authorValls, Claudia ( Orcid Icon 0000-0001-8279-1229 )
dc.date.accessioned2021-09-29T19:14:09Z
dc.date.available2021-09-29T19:14:09Z
dc.date.issued2020-06-03
dc.identifier.citationOliveira, R., & Valls, C. (2020). Global dynamics of the May-Leonard system with a Darboux invariant. Electronic Journal of Differential Equations, 2020(55), pp. 1-19.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14562
dc.description.abstractWe study the global dynamics of the classic May-Leonard model in ℝ3. Such model depends on two real parameters and its global dynamics is known when the system is completely integrable. Using the Poincaré compactification on ℝ3 we obtain the global dynamics of the classical May-Leonard differential system in ℝ3 when β = -1 - α. 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 Pointcaré ball, that is, the compactification of ℝ3 in the sphere S2 at infinity. We also describe the ω-limit and α-limit of each of the orbits. For some values of the parameter α 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 ω-limit. The same holds for the sixth and eighth octants.
dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectLotka-Volterra systemsen_US
dc.subjectMay-Leonard systemsen_US
dc.subjectDarboux invarianten_US
dc.subjectPhase portraitsen_US
dc.subjectLimit setsen_US
dc.subjectPoincare compactificationen_US
dc.titleGlobal dynamics of the May-Leonard system with a Darboux invarianten_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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