César Silva - Research

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Published/Accepted papers

·         (with S. Vaz and J. Mateus), A consistent discrete version of a non-autonomous SIRVS model, Discrete Dynamics in Nature and Society, accepted for publication

·         (with R. Ferreira), A nonautonomous epidemic model on time scales, J. Difference Equations and Applications, accepted for publication

·          (with S. Rosa, P. Rebelo, H. Alves and P. Guedes) Optimal control of the customer dynamics based on marketing policy, Appl. Math. Comput., accepted for publication

·         (with J. Mateus, P. Rebelo, S. Rosa and D. Torres) Optimal control of non-autonomous SEIRS models with vaccination and treatment, Discrete Contin. Dyn. Syst. S, accepted for publication

·         (with A. Bento and J. Oliveira) Nonuniform behavior and stability of Hopfield neural networks with delay, Nonlinearity 30 (2017), 3088–3103

·         (with A. Bento, N. Lupa and M. Megan) Integral conditions for nonuniform μ-dichotomy, Discrete Contin. Dyn. Syst. B 22 (2017), 3063–3077

·         Existence of Periodic Solutions for Eco-Epidemic Model with Disease in the Prey, J. Math. Anal. Appl. 453 (2017), 383-397

·         (with M. Bouhmadi-López, J. Marto and J. Morais), Cosmic infinity: A dynamical system approach, JCAP 03 (2017), 042

·         (with J. Mateus) Existence of periodic solutions of a periodic SEIRS model with general incidence, Nonlinear Analysis: Real World Applications, 34 (2017), 379–402

·         (with S. Rosa, H. Alves and P. Carvalho) A mathematical model for the customer dynamics based on marketing policy, Appl. Math. Comput., 273 (2016), 42–53

·         (with A. Bento) Nonuniform Dichotomic Behavior: Lipschitz Invariant Manifolds for Difference Equations, Portugaliae Mathematica, Port. Math. 73 (2016), 41–64.

·         (with J. Mateus) A Non-Autonomous SEIRS Model with General Incidence Rate, Appl. Math. Comput., 247 (2014), 169-189

·         A generalized epidemic model with latent stage and isolation, Math. Meth. Appl. Sci., 37 (2014), 1974–1991

·         (with A. Bento) Nonuniform Dichotomic Behavior: Lipschitz Invariant Manifolds for ODEs, Bulletin des Sciences Mathématiques, 138 (2014), 89–109

·         (with A. Bento) Generalized nonuniform dichotomies and local stable manifolds, J. Dyn. Diff. Equat. 25 (2013), 1139-1158

·         (with E. Pereira and J. Silva) A Generalized Non-Autonomous SIRVS Model, Math. Methods Appl. Sci., 36 (2013), 275-289

·         (with A. Bento)  Stable manifolds for nonautonomous equations with nonuniform polynomial dichotomies, Q. J. Math, 63 (2012), 275-308

·         (with M. BessaDense area preserving homeomorphisms have zero Lyapunov exponents, Discrete Contin. Dyn. Syst., 32, (2012), 1231-1244.

·         (with A. Bento)  Nonuniform (\mu,\nu)-dichotomies and local dynamics of difference equations, Nonlinear Anal., Theory Methods Appl., Ser. A, 75, (2012), 78-90.

·         (with A. Bento)  Stable Manifolds for Nonuniform Polynomial Dichotomies, J. Funct. Anal., 257 (2009), 122-14.

·         (with L. Barreira and C. Valls)  Nonuniform Behaviour and Robustness, J. Differential Equations, 246 (2009), 3579-3608.

·         (with L. Barreira and C. Valls)  Integral stable manifolds in Banach spaces, J. London Math. Soc., 77 (2008), 443-464.

·         (with L. Barreira and C. Valls)  Regularity of invariant manifolds for nonuniformly hyperbolic dynamics, J. Dynam. Differential Equations, 20 (2008), 281-299.

·         (with L. BarreiraLyapunov exponents for continuous transformations and dimension theory, Discrete Contin. Dyn. Syst. 13 (2005), 469-490.

Conference Proceedings

·         (with E. Pereira and J. Silva)  A Generalized Non-Autonomous SIRVS Model, Proceedings of the ICNAAM 2010, AIP Conference Proceedings, 1281 (2010), 583-586.

Submitted papers

·          (with A. Bento) Robustness of Discrete Nonuniform Dichotomic Behavior

·         (with A. Bento) Nonautonomous equations, generalized dichotomies and stable manifolds

Conferences/Seminars

 

·         Pode a matemática descrever uma epidemia?, Matemática do Planeta Terra 2013, Universidade da Beira Interior, Covilhã, 14 December 2013

·         General dichotomic behavior for trajectories of nonautonomous difference equations, Planet Earth, Dynamics, Games and Science 2013, Calouste Gulbenkian Foundation, Lisbon, 4 September 2013

·         General dichotomic behavior and C1 invariant manifolds, PODE2013, Bialystok University of Technology, Białystok, Poland, 25 July 2013

·         Robustness of general dichotomic behaviour, ICDEA2013, Sultan Qaboos University, Muscat, Oman, 29 May 2013

·         General dichotomic behavior for difference and differential equations, Universidade da Beira Interior, Covilhã, 31 September 2012

·         Invariant manifolds for perturbations of nonautonomous difference equations with general dichotomic behaviour, ECIT2012, Universidade dos Açores, Ponta Delgada, 13 September 2012

·         Global stable manifolds for difference equations with nonuniform (\mu,\nu)-dichotomies, Universidade do Minho, Braga, 22 February 2012

·         Global stable manifolds for difference equations with nonuniform (\mu,\nu)-dichotomies, PODE2011, Dublin City University, Dublin, Ireland, 22 May 2011.

·         A Generalized Non-Autonomous SIRVS Model, ICNAAM2010, Rhodes, Greece, 23 September 2010.

·         Existência e regularidade de variedades invariantes estáveis para perturbações de dicotomias exponenciais não-uniformes, Department of Pure Mathematics, Universidade do Porto, Porto, 11 April 2008.

·         Regularidade de variedades invariantes estáveis, Department of Mathematics, Universidade da Beira Interior, Covilhã, 28 de Março de 2007.

·         Expoentes de Lyapunov para transformações não necessariamente diferenciáveis, Department of Mathematics, Universidade da Beira Interior, Covilhã, 2003.

·         Construções geométricas e teoria de dimensão, Ergodic Theory and Dynamical Systems Seminar, Department of Mathematics, Instituto Superior Técnico, Lisbon, 2002.

·         Expoentes de Lyapunov e teorema ergódico multiplicativo,Ergodic Theory and Dynamical Systems Seminar, Department of Mathematics, Instituto Superior Técnico, Lisbon, 2002.

Other activities

Participation in the translation to Portuguese of the book "Introduction to the Modern Theory of Dynamical Systems" by A. Katok and B. Hasselblatt.