UMA UMA
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Rafael Domingos Garanito Luís

Faculty of Exact Sciences and Engineering

Penteada University Campus , Floor 2, Office 2.110

http://rafaelluismadeira.wix.com/rafaelluis

rafael.luis@staff.uma.pt

(+351) 291 705 161 / 5161

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Discipline today, results tomorrow

Biographical Notes

Rafael Luís obtained his PhD in Mathematics in 2011 from the University of Madeira (UMa), in the field of Mathematical Analysis, specializing in the Stability of Discrete Dynamical Systems. His dissertation is entitled ?Nonautonomous Difference Equations and Applications.? He is currently an Adjunct Assistant Professor (or equivalent) at the University of Madeira, where he teaches Mathematics courses for programmes such as Economics and Mathematics, among others.

He conducts research at the Center for Mathematical Analysis, Geometry and Dynamical Systems of the Instituto Superior Técnico, University of Lisbon, in the area of Discrete Dynamical Systems with applications to Biology and Economics. Recently, his research has focused on the global stability of discrete evolution models.

Publications

- Global asymptotic stability and bifurcation of an evolutionary Beverton-Holt model, Emma D'Aniello, Saber Elaydi, Eddy Kwessi, Rafael Luís, Brian Ryals, Journal of Difference Equations and Applications, 2025, 39

- Global asymptotic stability of evolutionary periodic Ricker competition models, Saber Elaydi, Yun Kang, Rafael Luís, Journal of Difference Equations and Applications, 2024, 26

- How far can we go in stability conditions for periodic maps?, Rafael Luís, The 29th International Conference on Difference Equations and Applications (ICDEA 2024), 2024

- Invariant Sets, Global Dynamics, and the Neimark?Sacker Bifurcation in the Evolutionary Ricker Model, Rafael Luís, Brian Ryals, Symmetry, 2024

- Local stability conditions for a n-dimensional periodic mapping, Rafael Luís, Sandra Mendonça, Mathematics and Computers in Simulation, 2024, 1615

- Open Problems and Conjectures in the Evolutionary Periodic Ricker Competition Model, Rafael Luís, Axioms, 2024

- A global picture for the planar Ricker map: convergence to fixed points and identification of the stable/unstable manifolds, Baigent, S., Z. Hou, S. Elaydi, E.C. Balreira, and R. Luís, J. Difference Equ. Appl, 2023, 17

- The effects of evolution on the stability of competing species., Elaydi, S.; Kang, Y.; Luís, R., Journal of Biological Dynamics, 2022, 24 16

- A STOCHASTIC STUDY FOR A GENERALIZED LOGISTIC MODEL, Rafael Luís and Sandra Mendonça, REVSTAT - STATISTICAL JOURNAL, 2021, 15

- Geometry and Global Stability of 2D Periodic Monotone Maps, Eduardo Balreira Cabral and Rafael Luís, Journal of Dynamics and Differential Equations, 2021

Academic Qualifications

- PhD in Matemática, 2011, University of Madeira

- Master Degree in Matemática, 2006, University of Madeira

- Undergraduate Degree in Matemática, 1999, University of Madeira