Fabio Scalco Dias, Regilene Oliveira, Claudia Valls
Abstract:
We study the May-Leonard asymmetric model in \(R^3\) which was introduced in [3,8].
It is the celebrated classical May-Leonard model incorporating asymmetric competitive
effects instead of requiring equal intrinsic growth rates for each competing population.
We study this system when it has an invariant of Darboux type and for these values of
the parameters we shall describe its global dynamics in the compactification of the
sphere, adding its infinity.
In particular, we study the dynamics of that system on the invariant planes
and we complete the study describing the dynamics at infinity.
We also prove that the system is completely integrable and describe the \(\alpha\)
and \(\omega\) limits of all the orbits of the system.
Submitted August 26, 2025. Published December 16, 2025.
Math Subject Classifications: 34A34, 34D23.
Key Words: Poincare compactification; phase portraits; dynamics at infinity; integrability.
DOI: 10.58997/ejde.2025.115
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Fabio Scalco Dias Instituto de Matemática e Computação Universidade Federal de Itajubá, Avenida BPS 1303 Pinheirinho, CEP 37.500-903, Itajubá, MG, Brazil email: scalco@unifei.edu.br |
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Regilene Oliveira Departamento de Matemática ICMC-Universidade de São Paulo Avenida Trabalhador São-carlense, 400 - 13566-590 São Carlos, SP, Brazil email: regilene@icmc.usp.br |
| Cláudia Valls Departamento de Matemática, Instituto SuperiorTécnico Universidade Técnica de Lisboa Av. Rovisco Pais 1049-001, Lisboa, Portugal email: claudia.valls@tecnico.pt |
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