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Identification

Personal identification

Full name
Rafael Luís

Citation names

  • Luís, Rafael

Author identifiers

Ciência ID
B41F-E943-D36D
ORCID iD
0000-0002-5991-9164
Google Scholar ID
https://scholar.google.pt/citations?hl=pt-PT&user=INSy4WymYBMC
Researcher Id
I-7093-2016
Scopus Author Id
35185293300

Telephones

Mobile phone
  • 966575645 (Personal)

Addresses

  • Gaula, 9100-213, Santa Cruz, Santa Cruz, Portugal (Personal)

Websites

Knowledge fields

  • Exact Sciences - Mathematics - Applied Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
French Elementary (A2) Intermediate (B1) Elementary (A2) Intermediate (B1) Elementary (A2)
Spanish; Castilian Elementary (A2) Elementary (A2) Elementary (A2) Elementary (A2) Elementary (A2)
Education
Degree Classification
2011/09/08
Concluded
 Matemática (Doutoramento)
Major in Especialidade: Análise Matemática
Universidade da Madeira, Portugal
"Non-autonomous Difference Equations - Aplications to Economical and Biological Sciences" (THESIS/DISSERTATION)
2004/09/01 - 2006/10/01
Concluded
 Ensino de Matemática no 3.º C. do Ensino Básico e no Secundário (Mestrado)
Universidade da Madeira, Portugal
"Equações de Diferenças e Aplicações" (THESIS/DISSERTATION)
1994/09/01 - 1999/08/31
Concluded
 Licenciatura em Matemática (Licenciatura)
Major in Ensino
Universidade da Madeira, Portugal
1991/09/01 - 1994/08/31
Concluded
 Curso Técnico Profissional de Contabilidade (Ensino secundário)
Escola Secundária de Francisco Franco, Portugal
 16
Affiliation

Science

Category
Host institution 		Employer
2011/11/01 - Current Researcher (Research) Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Teaching in Higher Education

Category
Host institution 		Employer
2015/09/01 - Current Assistant (University Teacher) Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia, Portugal
2000/09/01 - 2007/08/31 Invited Assistant (University Teacher) Universidade da Madeira, Portugal

Other Careers

Category
Host institution 		Employer
1998/09/01 - 2015/08/31 Professor do ensino básico e secundário (Professor do ensino básico e secundário) Secretaria Regional de Educação, Portugal
Projects

Grant

Designation Funders
2008/01/01 - 2011/09/30 NONAUTONOMOUS DIFFERENCE EQUATIONS: APPLICATIONS TO ECONOMICAL AND BIOLOGICAL SCIENCES
SFRH/BD/40924/2007
Universidade da Madeira, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded

Contract

Designation Funders
2019/01/01 - 2019/12/31 Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
UID/MAT/04459/2019
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2019/01/01 - 2019/12/31 Centro de Análise Matemática, Geometria e Sistemas Dinâmicos
UID/MAT/04459/2019
Universidade de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Conference paper
  1. Elaydi, S.N.; Luís, R.; Oliveira, H.. "Towards a theory of periodic difference equations and its application to population Dynamics". 2011.
    10.1007/978-3-642-11456-4_19
  2. Luís, Rafael. "A dynamical system for a long term economic model". 2011.
Journal article
  1. Emma D’Aniello; Saber Elaydi; Eddy Kwessi; Rafael Luís; Brian Ryals. "Global Dynamics and Bifurcation of an Evolutionary Beverton-Holt Model with the Allee Effect". Symmetry (2025): https://doi.org/10.3390/sym17111811.
    10.3390/sym17111811
  2. Emma D'Aniello; Saber Elaydi; Eddy Kwessi; Rafael Luís; Brian Ryals. "Global asymptotic stability and bifurcation of an evolutionary Beverton-Holt model". Journal of Difference Equations and Applications (2025): https://doi.org/10.1080/10236198.2025.2510550.
    10.1080/10236198.2025.2510550
  3. Rafael Luís; Brian Ryals. "Invariant Sets, Global Dynamics, and the Neimark–Sacker Bifurcation in the Evolutionary Ricker Model". Symmetry (2024): https://www.mdpi.com/2073-8994/16/9/1139.
    10.3390/sym16091139
  4. Rafael Luís. "Open Problems and Conjectures in the Evolutionary Periodic Ricker Competition Model". Axioms (2024): https://doi.org/10.3390/axioms13040246.
    10.3390/axioms13040246
  5. Rafael Luís; Sandra Mendonça. "Local stability conditions for a n-dimensional periodic mapping". Mathematics and Computers in Simulation (2024): https://doi.org/10.1016/j.matcom.2023.11.023.
    10.1016/j.matcom.2023.11.023
  6. Saber Elaydi; Yun Kang; Rafael Luís. "Global asymptotic stability of evolutionary periodic Ricker competition models". Journal of Difference Equations and Applications (2023): https://doi.org/10.1080/10236198.2023.2281552.
    10.1080/10236198.2023.2281552
  7. E. Cabral Balreira; Rafael Luís. "Geometry and Global Stability of 2D Periodic Monotone Maps". Journal of Dynamics and Differential Equations 35 3 (2023): 2185-2198. http://dx.doi.org/10.1007/s10884-021-10089-z.
    10.1007/s10884-021-10089-z
  8. S. Baigent; Z. Hou; S. Elaydi; E. C. Balreira; R. Luís. "A global picture for the planar Ricker map: convergence to fixed points and identification of the stable/unstable manifolds". Journal of Difference Equations and Applications (2023): https://doi.org/10.1080/10236198.2023.2222855.
    10.1080/10236198.2023.2222855
  9. S. Elaydi; Y. Kang; R. Luís. "The effects of evolution on the stability of competing species". Journal of Biological Dynamics (2022): https://doi.org/10.1080/17513758.2022.2154860.
    10.1080/17513758.2022.2154860
  10. Rafael Luís. "Linear Stability Conditions for a First Order n-Dimensional Mapping". Qualitative Theory of Dynamical Systems 20 1 (2021): https://doi.org/10.1007/s12346-021-00455-z.
    10.1007/s12346-021-00455-z
  11. Luís, Rafael; Mendonça, Sandra. Corresponding author: Luís, Rafael. "A Stochastic Study for a Generalized Logistic Model". REVSTAT - Statistical Journal 19 1 (2021): 71-85.
    Published
  12. Rafael Luis da SILVA; Carlos Edwar de Carvalho FREITAS; Sandrelly Oliveira INOMATA; Lucirene Aguiar de SOUZA; Raniere Garcez Costa SOUSA. "MODELING OF FISH SEIZURES AFTER THE IMPLEMENTATION OF THE CLOSED FISHING SEASON LAW IN THE AMAZON BASIN". Boletim do Instituto de Pesca (2020): https://doi.org/10.20950/1678-2305.2020.46.3.588.
    10.20950/1678-2305.2020.46.3.588
  13. Luís, Rafael. "A note on global stability in the periodic logistic map". Discrete & Continuous Dynamical Systems - B (2020): http://dx.doi.org/10.3934/dcdsb.2020094.
    10.3934/dcdsb.2020094
  14. E. Cabral Balreira; Saber Elaydi; Rafael Luís. "Global stability of higher dimensional monotone maps". Journal of Difference Equations and Applications (2017): 1-35. https://doi.org/10.1080/10236198.2017.1388375.
    10.1080/10236198.2017.1388375
  15. Rafael Luís; Elias Rodrigues. "Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model". Discrete Dynamics in Nature and Society (2017):
    10.1155/2017/6186354
  16. Luís, Rafael. "A SURVEY ON THE ENVELOPING METHOD OF SOME ONE-DIMENSIONAL NON-AUTONOMOUS DISCRETE PERIODIC POPULATION MODELS". Journal of Mathematical Sciences: Advances and Applications (2016): http://www.scientificadvances.co.in/artical/1/193.
    10.18642/jmsaa_7100121662
  17. Luís, R.. "On the global dynamics of periodic triangular maps". Journal of Difference Equations and Applications (2016): 1-15. http://www.scopus.com/inward/record.url?eid=2-s2.0-84975222089&partnerID=MN8TOARS.
    10.1080/10236198.2016.1198343
  18. Luís, Rafael; Mendonça, Sandra. "A note on the bifurcation point of a randomized Fibonacci model". Chaotic Modeling and Simulations (CMSIM) 4 (2016): 445-458. http://www.cmsim.eu/papers_pdf/october_2016_papers/4.Luis_Mentonca_445-458.pdf.
    Published
  19. Cabral Balreira, E.; Elaydi, S.; Luís, R.. "Global dynamics of triangular maps". Nonlinear Analysis, Theory, Methods and Applications 104 (2014): 75-83. http://www.scopus.com/inward/record.url?eid=2-s2.0-84898604853&partnerID=MN8TOARS.
    10.1016/j.na.2014.03.019
  20. Luís, R.; Oliveira, H.M.. "Products of 2 × 2 matrices related to non autonomous Fibonacci difference equations". Applied Mathematics and Computation 226 (2014): 101-116. http://www.scopus.com/inward/record.url?eid=2-s2.0-84888079304&partnerID=MN8TOARS.
    10.1016/j.amc.2013.09.075
  21. Cabral Balreira, E.; Elaydi, S.; Luís, R.. "Local stability implies global stability for the planar Ricker competition model". Discrete and Continuous Dynamical Systems - Series B 19 2 (2014): 323-351. http://www.scopus.com/inward/record.url?eid=2-s2.0-84894233536&partnerID=MN8TOARS.
    10.3934/dcdsb.2014.19.323
  22. Elaydi, S.; Luís, R.; Oliveira, H.. "Local bifurcation in one-dimensional nonautonomous periodic difference equations". International Journal of Bifurcation and Chaos 23 3 (2013): http://www.scopus.com/inward/record.url?eid=2-s2.0-84876246634&partnerID=MN8TOARS.
    10.1142/S0218127413500491
  23. Guzowska, M.; Luís, R.; Elaydi, S.. "Bifurcation and invariant manifolds of the logistic competition model". Journal of Difference Equations and Applications 17 12 (2011): 1851-1872. http://www.scopus.com/inward/record.url?eid=2-s2.0-84855821709&partnerID=MN8TOARS.
    10.1080/10236198.2010.504377
  24. Elaydi, S.; Luís, R.. "Erratum to Open problems in some competition models". Journal of Difference Equations and Applications 17 12 (2011): http://www.scopus.com/inward/record.url?eid=2-s2.0-84855811744&partnerID=MN8TOARS.
    10.1080/10236198.2011.585985
  25. Elaydi, S.; Luís, R.. "Open problems in some competition models". Journal of Difference Equations and Applications 17 12 (2011): 1873-1877. http://www.scopus.com/inward/record.url?eid=2-s2.0-84855777437&partnerID=MN8TOARS.
    10.1080/10236198.2011.559468
  26. Oliveira, H.; Luís, R.. "A discrete dynamical system for the Marx model". Journal of Difference Equations and Applications 17 8 (2011): 1199-1206. http://www.scopus.com/inward/record.url?eid=2-s2.0-80051971579&partnerID=MN8TOARS.
    10.1080/10236190903052888
  27. Luís, R.; Elaydi, S.; Oliveira, H.. "Stability of a Ricker-type competition model and the competitive exclusion principle". Journal of Biological Dynamics 5 6 (2011): 636-660. http://www.scopus.com/inward/record.url?eid=2-s2.0-80052037918&partnerID=MN8TOARS.
    10.1080/17513758.2011.581764
  28. Luís, R.; Elaydi, S.; Oliveira, H.. "Non-autonomous periodic systems with allee effects". Journal of Difference Equations and Applications 16 10 (2010): 1179-1196. http://www.scopus.com/inward/record.url?eid=2-s2.0-77956809452&partnerID=MN8TOARS.
    10.1080/10236190902794951
  29. Luís, R.; Elaydi, S.; Oliveira, H.. "An economical model with Allee effect". Journal of Difference Equations and Applications 15 8-9 (2009): 877-894. http://www.scopus.com/inward/record.url?eid=2-s2.0-70549106691&partnerID=MN8TOARS.
    10.1080/10236190802468920
  30. Borges, Cátia; Correia, Carla; Garapa, Marco; Luís, Rafael. "Dimensão de Hausdorff da linha da costa da ilha do Porto Santo". Boletim da Sociedade Portuguesa de Matemática 42 (2000): 5-14.
Thesis / Dissertation
  1. Luís, Rafael Domingos Garanito. "Nonautonomous difference equations with applications". PhD, 2011. http://hdl.handle.net/10400.13/206.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2021/07/29 Linear stability conditions for a first order n-dimensional mapping ICDEA2021 - International Conference on Difference Equations and Applications
International Society on Difference Equations and Dynamical Systems (Sarajevo, Bosnia and Herzegovina)
2018/07/11 Stability and Bifurcation in Discrete Dynamical Systems: Application to Competition Population Models ICMA18 - 1st International Conference on Mathematical Applications 18
Universidade da Madeira (Funchal, Portugal)
2017/09/12 Local Stability in 3D discrete dynamical systems: applications to population models SIMBioS - Stochastic and Deterministic Mathematical Methods for Biological and Environmental Systems: Theory & Applications
Universidade da Madeira (Funchal, Portugal)
2016/07/25 Recent advances in global stability of monotone maps: Application to population dynamics 22nd International Conference on Difference Equations and Applications - ICDEA2016
Osaka Prefecture University (Osaka, Japan)
2016/07/22 Recent advances in global stability of monotone maps: Application to population dynamics 2nd International Satelite Conference on Difference Equations and Applications
Okayama University of Science (Okayama, Japan)
2015/07/20 Global Stability of Higher Dimensional Monotone Models: Applications to Leslie-Gower and Ricker Competitions Models 21st International Conference on Difference Equations and Applications
(Bialystok, Poland)
2013/07/22 Local bifurcation in one dimensional nonautonomous periodic difference equations Progress on Difference Equations 2013-PODE 2013
(Bialystok, Poland)
2012/07/22 Local stability implies global stability in the Ricker competition model 18th International Conference on Difference Equations and Applicationms - ICDEA2012
(Barcelona, Spain)
2011/07/25 Bifurcations in one-dimensional periodic difference equations 17th International Conference on Difference Equations and Applications - ICDEA 2011
(Trois-Rivière, Quebéc, Canada)
2010/07/22 The bifurcation scenario of the periodic Ricker-type competition model 6th International Conference on Difference Equations and Applications - ICDEA 2010
(Riga, Latvia)
2010/05/22 A note on the bifurcations curves of the periodic Ricker map Progress on Difference Equations 2010
(Xanthi, Greece)
2009/10/22 Nonautonomous periodic Leslie-Gower competition model 15th International Conference on Difference Equations and Applications - ICDEA15
(Estoril, Portugal)
2009/05/25 Nonautonomous periodic systems with the Cantor set property Progess on Difference Equations 2009
(Bedlewo, Poland)
2009/01/07 Nonautonomous periodic difference equations with applications in biology Special session on Discrete Dynamical Systems in Periodic Environments, during the Joint Mathematics Meetings
(Washington, United States)
2008/09/09 Nonautonomous periodic systems with Allee effects- Revisited Dynamics & Applications - DYNA2008
(Braga, Portugal)
2008/07/24 Nonautonomous periodic systems with Allee effects 14th International Conference on Difference Equations and Applications - ICDEA14
(Istambul, Turkey)
2007/07/26 A Dynamical System for a Long Term Economic Model 12nd International Conference on Difference Equations and Applications - ICDEA 12
(Lisboa, Portugal)
2007/03/16 An economic model with Allee effect Progess on Difference Equations
(Laufen, Germany)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2021/09/01 - 2023/12 A Dinâmica do Modelo Populacional de Ricker.
Supervisor
 Matemática, Estatística e Aplicações (Master)
Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia, Portugal
2019/09/01 - 2020/08/31 Sistemas Dinâmicos Não-lineares e Aplicações
Supervisor
 Matemática, Estatística e Aplicações (Master)
Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia, Portugal
2018/09/01 - 2020/02 Modelos Matemáticos Discretos Aplicados à Dinâmica de Populações
Supervisor
 Matemática, Estatística e Aplicações (Master)
Universidade da Madeira Faculdade de Ciências Exatas e da Engenharia, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2013/09/01 - 2014/12/15 MadeiraMat2014 (2014/07/03 - 2014/07/04)
Congress (Member of the Organising Committee)
 Núcleo Regional da Madeira da Associação de Professores de Matemática, Portugal
2009/09/01 - 2009/11/30 International Conference on Diference Equatios and Applicatios, ICDEA15 (2009/10/19 - 2009/10/23)
Congress (Co-organisor)
 Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal
2007/07/15 - 2007/07/31 International Conference on Diference Equations and Applications, ICDEA12 (2007/07/23 - 2007/07/29)
Congress (Co-organisor)
 Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal

Event participation

Activity description
Type of event 		Event name
Institution / Organization
2021/07/26 - 2021/07/30 International Conference on Difference Equations and Applications (Virtual)
Conference
 ICDEA 2021
2018/07/09 - 2018/07/12 1st International Conference on Mathematical Applications
Conference
 ICMA18
Universidade da Madeira Madeira Interactive Technologies Institute, Portugal
2017/09/11 - 2017/11/15 Stochastic and Deterministic Mathematical Methods for Biological and Environmental Systems: Theory & Applications
Conference
 SIMBioS
Universidade da Madeira Centro de Ciências Matemáticas, Portugal
2016/07/24 - 2016/07/29 22nd International Conference on Difference Equations and Applications
Conference
 ICDEA 2016
2016/07/22 - 2016/07/23 2nd International Satelite Conference on Difference Equations and Applications
Conference
2015/07/19 - 2015/07/25 21st International Conference on Difference Equations and Applications
Conference
 ICDEA 2015
2013/06/21 - 2013/06/26 Progress on Difference Equations
Conference
 PODE 2013
2012/07/22 - 2012/07/27 18th International Conference on Difference Equations and Applicationms
Conference
 ICDEA2012
2011/07/24 - 2011/07/29 International Conference on Difference Equations and Applications
Conference
 ICDEA 2001
2010/07/19 - 2010/07/23 International Conference on Difference Equations and Applications
Conference
 ICDEA 2010
2010/05/21 - 2010/05/25 Progress on Difference Equations PODED 2010
2009/10/19 - 2009/10/23 International Conference on Difference Equations and Applications - ICDEA15
Centro de Análise Matemática Geometria e Sistemas Dinâmicos, Portugal
2009/01/05 - 2009/01/08 "Nonautonomous periodic difference equations with applications in biology”, in a special session on "Discrete Dynamical Systems in Periodic Environments", during the Joint Mathematics Meetings, in Washington, DC.
Conference
 Special session on Discrete Dynamical Systems in Periodic Environments, during the Joint Mathematics Meetings
American Mathematical Society, United States
2008/07/21 - 2008/07/25 International Conference on Difference Equations and Applications
Conference
 International Conference on Difference Equations and Applications
2008/03/12 - 2008/03/17 Progress on Difference Equations
Congress
 Progress on Difference Equations - PODE 2008
2007/07/23 - 2007/07/27 International Conference on Difference Equations and Applications - ICDEA 12
Congress
 International Conference on Difference Equations and Applications - ICDEA 12
2007/07/23 - 2007/07/27 International Conference on Difference Equations and Applications - ICDEA 12
Congress
 12nd International Conference on Difference Equations and Applications

Ad Hoc journal article review

Journal title (ISSN) Publisher
2023/08/01 - Current Nonautonomous Dynamical Systems ( 2353-0626) De Gruyter Open Access
2021/05/02 - Current Mathematical Methods in the Applied Sciences (0170-4214) WILEY
2021/01/01 - Current Entropy (1099-4300 ) MDPI
2020/01/01 - Current Qualitative Theory of Dynamical Systems (1662-3592) Springer
2018/01/01 - Current Energies (1996-1073 ) MDPI
2018/01/01 - Current Chaos, Solitons and Fractals (0960-0779) Elsevier
2016/05/03 - Current Advances in Difference Equations (1687-1847) Springer
2015/01/01 - Current Fractals (0218-348X) World Scientific
2015/01/01 - Current PLOS ONE (1932-6203)
2013/05/21 - Current Nonlinear Analysis: Real World Applications (1468-1218) ScienceDirect
2013/03/01 - Current Journal of Biological Dynamics (1751-3758 ) Taylor and Francis
2012/01/01 - Current Journal of Difference Equations and Applications (1023-6198) Taylor & Francis

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2021/09 - Current Matemática I para a Economia Economia (Licenciatura) Universidade da Madeira, Portugal
2020/09/10 - Current Álgebra para a Economia Economia (Licenciatura) Universidade da Madeira, Portugal
2015/09/12 - Current Matemática II para a Economia Economia (Licenciatura) Universidade da Madeira, Portugal
2023/09/12 - 2024/01/26 Análise Matemática I Matemática (Licenciatura) Universidade da Madeira, Portugal
2023/02 - 2023/07 Matemática II Gestão (Licenciatura) Universidade da Madeira, Portugal
2022/09 - 2023/02 Matemática I Gestão (Licenciatura) Universidade da Madeira, Portugal
2022/02 - 2022/07 Matemática VI Educação Básica (Licenciatura) Universidade da Madeira, Portugal
2021/02 - 2021/07 Matemática e Aplicações a Outras Ciências Matemática, Estatística e Aplicações (Mestrado integrado) Universidade da Madeira, Portugal
2015/09 - 2021/02 Matemática geral Bioquímica (Licenciatura) Universidade da Madeira, Portugal
2019/09 - 2020/02 Cálculo Eng Civil+Eng Electrónica e Telecomunicações+Eng Informática+Matemática (Licenciatura) Universidade da Madeira, Portugal
2015/09 - 2020/02 Matemáticas Gerais Biologia (Licenciatura) Universidade da Madeira, Portugal
2019/02 - 2019/07 Matemática e Aplicações a outras Ciências Matemática, Estatística e Aplicações (Mestrado integrado) Universidade da Madeira, Portugal
2018/09 - 2019/02 Estatística I Psicologia (Licenciatura) Universidade da Madeira, Portugal
2018/02 - 2018/07 Matemática II Gestão (Licenciatura) Universidade da Madeira, Portugal
2015/09 - 2016/02 Matemática I Psicologia (Licenciatura) Universidade da Madeira, Portugal