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Identification

Personal identification

Full name
César Augusto Teixeira Marques da Silva

Citation names

  • Silva, César M.

Author identifiers

Ciência ID
A617-5B18-86CC
ORCID iD
0000-0001-6189-8836

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
Portuguese (Mother tongue)
English Upper intermediate (B2) Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
French Elementary (A2) Intermediate (B1) Elementary (A2) Intermediate (B1)
Education
Degree Classification
2003 - 2007
Concluded
 Matemática (Doutoramento)
Universidade de Lisboa Instituto Superior Técnico, Portugal
"Expoentes de Lyapunov, hiperbolicidade não-uniforme e variedades invariantes estáveis" (THESIS/DISSERTATION)
2000 - 2002
Concluded
 Matemática Aplicada (Mestrado)
Major in Sistemas Dinâmicos
Universidade de Lisboa Instituto Superior Técnico, Portugal
"Expoentes de Lyapunov para transformações contínuas" (THESIS/DISSERTATION)
1994 - 2000
Concluded
 Matemática Aplicada e Computação (Licenciatura)
Major in Análise Matemática
Universidade de Lisboa Instituto Superior Técnico, Portugal
 15
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2021 - Current Associate Professor (University Teacher) Universidade da Beira Interior, Portugal
2007 - 2021 Assistant Professor (University Teacher) Universidade da Beira Interior, Portugal
2002 - 2007 Assistant (University Teacher) Universidade da Beira Interior, Portugal
2000 - 2002 Trainee Assistant (University Teacher) Universidade da Beira Interior, Portugal
Projects

Contract

Designation Funders
2019/01/01 - 2019/12/31 Centro de Matemática e Aplicações da Universidade da Beira Interior
UID/MAT/00212/2019
Universidade da Beira Interior, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 212 - 2011-2012
PEst-OE/MAT/UI0212/2011
Universidade da Beira Interior, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Conference paper
  1. Silva, C.M.; Pereira, E.; Da Silva, J.A.L.. "A generalized non-autonomous SIRVS model". 2010.
    10.1063/1.3498543
Journal article
  1. César M. Silva. "Nonuniform µ-dichotomy spectrum and kinematic similarity". Journal of Differential Equations (2023): https://doi.org/10.1016/j.jde.2023.08.015.
    10.1016/j.jde.2023.08.015
  2. Bento, António J.G.; Oliveira, José J.; Silva, César M.. "Existence and stability of a periodic solution of a general difference equation with applications to neural networks with a delay in the leakage terms". Communications in Nonlinear Science and Numerical Simulation 126 (2023): 107429. http://dx.doi.org/10.1016/j.cnsns.2023.107429.
    10.1016/j.cnsns.2023.107429
  3. de Jesus, Lopo F.; Silva, César Marques; Vilarinho, Helder. "An eco-epidemiological model with general functional response of predator to prey". Mathematical Methods in the Applied Sciences 46 4 (2022): 4085-4110. http://dx.doi.org/10.1002/mma.8743.
    10.1002/mma.8743
  4. de Jesus, Lopo F. ; Vilarinho, Helder; Silva, César. "Random perturbations of an eco-epidemiological model". Discrete & Continuous Dynamical Systems - B 27 1 (2022): 257-257. http://dx.doi.org/10.3934/dcdsb.2021040.
    10.3934/dcdsb.2021040
  5. Paulo Rebelo; Silvério Rosa; César M. Silva. "Modelling optimal pest control of non-autonomous predator-prey interaction". Mathematical Modelling of Natural Phenomena (2022): https://doi.org/10.1051/mmnp/2022033.
    10.1051/mmnp/2022033
  6. de Jesus, Lopo F.; Silva, César M.; Vilarinho, Helder. "Dynamics of a discrete eco-epidemiological model with disease in the prey". Journal of Difference Equations and Applications 27 1 (2021): 132-155. http://dx.doi.org/10.1080/10236198.2021.1876682.
    10.1080/10236198.2021.1876682
  7. Silva, César M.. "Admissibility and generalized nonuniform dichotomies for discrete dynamics". Communications on Pure & Applied Analysis 20 10 (2021): 3419. http://dx.doi.org/10.3934/cpaa.2021112.
    10.3934/cpaa.2021112
  8. de Jesus, Lopo; Silva, César; Vilarinho, Helder. "Periodic orbits for periodic eco-epidemiological systems with infected prey". Electronic Journal of Qualitative Theory of Differential Equations 54 (2020): 1-20. http://dx.doi.org/10.14232/ejqtde.2020.1.54.
    10.14232/ejqtde.2020.1.54
  9. Bessa, Mário; Silva, César; Vilarinho, Helder. "Stretching Generic Pesin's Entropy Formula". Journal of Statistical Physics 173 5 (2018): 1523-1546. http://dx.doi.org/10.1007/s10955-018-2163-1.
    10.1007/s10955-018-2163-1
  10. Rosa, S.; Rebelo, P.; Silva, C.M.; Alves, H.; Carvalho, P.G.. "Optimal control of the customer dynamics based on marketing policy". Applied Mathematics and Computation 330 (2018): 42-55. http://dx.doi.org/10.1016/j.amc.2018.02.027.
    10.1016/j.amc.2018.02.027
  11. Mateus, Joaquim; Silva, César M.; Vaz, S.. "A Consistent Discrete Version of a Nonautonomous SIRVS Model". Discrete Dynamics in Nature and Society 2018 (2018): 1-18. http://dx.doi.org/10.1155/2018/8152032.
    10.1155/2018/8152032
  12. Ferreira, Rui A. C.; Silva, César M.. "A nonautonomous epidemic model on time scales". Journal of Difference Equations and Applications 24 8 (2018): 1295-1317. http://dx.doi.org/10.1080/10236198.2018.1479400.
    10.1080/10236198.2018.1479400
  13. P. Mateus, Joaquim; Rebelo, Paulo; Rosa, Silvério; M. Silva, César; F. M. Torres, Delfim. "Optimal control of non-autonomous SEIRS models with vaccination and treatment". Discrete & Continuous Dynamical Systems - S 11 6 (2018): 1179-1199. http://dx.doi.org/10.3934/dcdss.2018067.
    10.3934/dcdss.2018067
  14. César M. Silva. "Existence of periodic solutions for periodic eco-epidemic models with disease in the prey". Journal of Mathematical Analysis and Applications 453 1 (2017): 383-397. https://doi.org/10.1016/j.jmaa.2017.03.074.
    10.1016/j.jmaa.2017.03.074
  15. Bento, António J G; Oliveira, José J; Silva, César M. "Nonuniform behavior and stability of Hopfield neural networks with delay". Nonlinearity 30 8 (2017): 3088-3103. http://dx.doi.org/10.1088/1361-6544/aa773b.
    10.1088/1361-6544/aa773b
  16. Joaquim P. Mateus; César M. Silva. "Existence of periodic solutions of a periodic SEIRS model with general incidence". Nonlinear Analysis: Real World Applications 34 (2017): 379-402. https://doi.org/10.1016/j.nonrwa.2016.09.013.
    10.1016/j.nonrwa.2016.09.013
  17. Bouhmadi-López, Mariam; Marto, João; Morais, João; Silva, César M.. "Cosmic infinity: a dynamical system approach". Journal of Cosmology and Astroparticle Physics 2017 03 (2017): 042-042. http://dx.doi.org/10.1088/1475-7516/2017/03/042.
    10.1088/1475-7516/2017/03/042
  18. J.G. Bento, António; Lupa, Nicolae; Megan, Mihail; M. Silva, César. "Integral conditions for nonuniform $µ$-dichotomy on the half-line". Discrete & Continuous Dynamical Systems - B 22 8 (2017): 3063-3077. http://dx.doi.org/10.3934/dcdsb.2017163.
    10.3934/dcdsb.2017163
  19. César M. Silva; Silvério Rosa; Helena Alves; Pedro G. Carvalho. "A mathematical model for the customer dynamics based on marketing policy". Applied Mathematics and Computation 273 (2016): 42-53. https://doi.org/10.1016%2Fj.amc.2015.09.050.
    10.1016/j.amc.2015.09.050
  20. Bento, A.J.G.; Silva, C.M.. "Nonuniform dichotomic behavior: Lipschitz invariant manifolds for difference equations". Portugaliae Mathematica 73 1 (2016): 41-64. http://www.scopus.com/inward/record.url?eid=2-s2.0-84959524473&partnerID=MN8TOARS.
    10.4171/PM/1975
  21. Silva, C.M.. "A nonautonomous epidemic model with general incidence and isolation". Mathematical Methods in the Applied Sciences 37 13 (2014): 1974-1991. http://www.scopus.com/inward/record.url?eid=2-s2.0-84904741897&partnerID=MN8TOARS.
    10.1002/mma.2950
  22. Mateus, J.P.; Silva, C.M.. "A non-autonomous SEIRS model with general incidence rate". Applied Mathematics and Computation 247 (2014): 169-189. http://www.scopus.com/inward/record.url?eid=2-s2.0-84907546531&partnerID=MN8TOARS.
    10.1016/j.amc.2014.08.078
  23. Pereira, E.; Silva, C.M.; Da Silva, J.A.L.. "A generalized nonautonomous SIRVS model". Mathematical Methods in the Applied Sciences 36 3 (2013): 275-289. http://www.scopus.com/inward/record.url?eid=2-s2.0-84873086717&partnerID=MN8TOARS.
    10.1002/mma.2586
  24. Bento, A.J.G.; Silva, C.M.. "Nonuniform dichotomic behavior: Lipschitz invariant manifolds for ODEs". Bulletin des Sciences Mathematiques (2013): http://www.scopus.com/inward/record.url?eid=2-s2.0-84884959626&partnerID=MN8TOARS.
    10.1016/j.bulsci.2013.09.008
  25. Bento, A.J.G.; Silva, C.M.. "Generalized Nonuniform Dichotomies and Local Stable Manifolds". Journal of Dynamics and Differential Equations 25 4 (2013): 1139-1158. http://www.scopus.com/inward/record.url?eid=2-s2.0-84890425365&partnerID=MN8TOARS.
    10.1007/s10884-013-9331-4
  26. Bento, A.J.G.; Silva, C.M.. "Stable manifolds for non-autonomous equations with non-uniform polynomial dichotomies". Quarterly Journal of Mathematics 63 2 (2012): 275-308. http://www.scopus.com/inward/record.url?eid=2-s2.0-80053999931&partnerID=MN8TOARS.
    10.1093/qmath/haq047
  27. Bessa, M.; Silva, C.M.. "Dense area-preserving homeomorphisms have zero lyapunov exponents". Discrete and Continuous Dynamical Systems 32 4 (2012): 1231-1244. http://www.scopus.com/inward/record.url?eid=2-s2.0-84859520465&partnerID=MN8TOARS.
    10.3934/dcds.2012.32.1231
  28. Bento, A.J.G.; Silva, C.M.. "Nonuniform (µ, ¿) -dichotomies and local dynamics of difference equations". Nonlinear Analysis, Theory, Methods and Applications 75 1 (2012): 78-90. http://www.scopus.com/inward/record.url?eid=2-s2.0-80054003922&partnerID=MN8TOARS.
    10.1016/j.na.2011.08.008
  29. Bento, A.J.G.; Silva, C.. "Stable manifolds for nonuniform polynomial dichotomies". Journal of Functional Analysis 257 1 (2009): 122-148. http://www.scopus.com/inward/record.url?eid=2-s2.0-64849112132&partnerID=MN8TOARS.
    10.1016/j.jfa.2009.01.032
  30. Barreira, L.; Silva, C.; Valls, C.. "Nonuniform behavior and robustness". Journal of Differential Equations 246 9 (2009): 3579-3608. http://www.scopus.com/inward/record.url?eid=2-s2.0-63149135780&partnerID=MN8TOARS.
    10.1016/j.jde.2008.10.009
  31. Barreira, L.; Silva, C.; Valls, C.. "Regularity of invariant manifolds for nonuniformly hyperbolic dynamics". Journal of Dynamics and Differential Equations 20 2 (2008): 281-299. http://www.scopus.com/inward/record.url?eid=2-s2.0-43449098150&partnerID=MN8TOARS.
    10.1007/s10884-007-9088-8
  32. Barreira, L.; Silva, C.; Valls, C.. "Integral stable manifolds in Banach spaces". Journal of the London Mathematical Society 77 2 (2008): 443-464. http://www.scopus.com/inward/record.url?eid=2-s2.0-44649151783&partnerID=MN8TOARS.
    10.1112/jlms/jdm120
  33. Barreira, L.; Silva, C.. "Lyapunov exponents for continuous transformations and dimension theory". Discrete and Continuous Dynamical Systems 13 2 (2005): 469-490. http://www.scopus.com/inward/record.url?eid=2-s2.0-23844437390&partnerID=MN8TOARS.
Activities

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2021/09/01 - Current Convergence of asymptotic systems: applications to neural network and biological models with delays.
Supervisor of Ahmed Osama Mohamed Sayed Sayed Elmwafy
 3.º ciclo em Matemática e Aplicações (PhD)
Universidade da Beira Interior Centro de Matemática e Aplicações, Portugal
2018 - 2021/07/05 Dynamics of Eco-Epidemiological Models
Supervisor of Lopo Ferreira de Jesus
 3.º ciclo em Matemática e Aplicações (PhD)
Universidade da Beira Interior, Portugal
2017 - 2018 Modelos Epidemiológicos SIR e SIS Discretos - Estudo dos modelos e elaboração de uma ação de divulagação na área da Biomatemática
Supervisor of Rabilde de Fátima Manuel Bartolomeu
 2.º ciclo em Matemática para Professores (Master)
Universidade da Beira Interior, Portugal
2017 - 2018 Modelos Ecológicos Unidimensionais - Estudo dos modelos e elaboração de uma ação de divulgação na área da Biomatemática
Supervisor of Augusto Veríssimo Víctor dos Santos
 2.º ciclo em Matemática para Professores (Master)
Universidade da Beira Interior, Portugal
2012 - 2016/02/23 Dynamics of Non-Autonomous SEIRS Models with General Incidence
Supervisor of Joaquim Manuel Pereira Mateus
 3.º ciclo em Matemática Aplicada (PhD)
Universidade da Beira Interior, Portugal
2010 - 2011 Dimensão de Hausdorff, capacidades e ferraduras de Smale
Supervisor of Gonçalo Calvário Fiadeiro Carreira
 2.º ciclo em Matemática no 3.º Ciclo do Ensino Básico e no Ensino Secundário (Master)
Universidade da Beira Interior, Portugal
2009 - 2010 Códigos detectores e correctores de erros
Supervisor of Carla dos Anjos Miranda
 2.º ciclo em Matemática no 3.º Ciclo do Ensino Básico e no Ensino Secundário (Master)
Universidade da Beira Interior, Portugal