Publications/Publicações

Research interests

• Symmetric Dynamical Systems -- Bifurcation theory with symmetry
  Special interest: the role of the symmetry in the study of the steady-state and Hopf bifurcations occurring in bifurcations problems symmetric under compact groups.
• Coupled Cell Systems
  Special interest: the study of the dynamics and bifurcations of sets of cells (systems of ordinary differential equations) that are coupled together exploring the role of the coupled cell network representing the cells and the interactions between them, and the internal cell dynamics. The coupled cell networks can have symmetry, interior symmetries and groupoid symmetries.

Theses

A.P.S.Dias, 1993. Caos Instantâneo, MSc dissertation, Universidade do Porto, Portugal.

A.P.S.Dias, 1997. Bifurcations with wreath product symmetry, PhD Thesis, Math. Institute, University of Warwick, UK. pdf

Papers

I.S.Labouriau and A.P.S.Dias. Instant chaos is chaos in slow motion, Journal of Mathematical Analysis and Applications 199 (1996) 138-48.

A.P.S.Dias. Hopf bifurcation for wreath products, Nonlinearity 11 (1998) 247-264. pdf

A.P.S.Dias and I.Stewart. Hopf bifurcation on a simple cubic lattice, Dynamics and Stability of Systems 14 (1999) 3-55. pdf

A.P.S.Dias and I.Stewart. Symmetry-breaking Bifurcations of Wreath Product Systems, Journal of Nonlinear Science 9 (1999) 671-695. pdf

A.P.S.Dias and I.Stewart. Invariant Theory for Wreath Product Groups, Journal of Pure and Applied Algebra 150 (2000) 61-84. pdf

I.Stewart and A.P.S.Dias. Hilbert Series for Equivariant Mappings Restricted to Invariant Hyperplanes, Journal of Pure and Applied Algebra 151 (2000) 89-106. pdf

I.Stewart and A.P.S.Dias. Toric Geometry and Equivariant Bifurcations, Physica D 143 (2000) 235-261. pdf

A.P.S.Dias, B.Dionne and I.Stewart. Heteroclinic Cycles and Wreath Product Symmetries, Dynamics and Stability of Sytems 15 (2000) 353-385. pdf

A.P.S.Dias and I.Stewart. Secondary bifurcations in systems with All-to-All coupling, Proceedings of the Royal Society of London Ser. A 459 (2003) 1-18. pdf

A.P.S.Dias and I.Stewart. Symmetry Groupoids and Admissible Vector Fields for Coupled Cell Networks, Journal of the London Mathematical Society 69 (2004) 707-736. pdf

A.P.S.Dias and I.Stewart. Linear Equivalence and ODE-equivalence for Coupled Cell Networks, Nonlinearity 18 (2005) 1003-1020. pdf

F.Antoneli, A.P.S.Dias, M.Golubitsky and Y.Wang. Patterns of Synchrony in Lattice Dynamical Systems, Nonlinearity 18 (2005) 2193-2209. pdf

S.M.C.Abreu and A.P.S.Dias. Hopf Bifurcation on Hemispheres. Nonlinearity 19 (2006) 553-574. pdf

A.P.S.Dias and R.C.Paiva. Hopf bifurcation with D_n-symmetry. Glasgow Mathematical Journal 48 (2006) 41-51. pdf

A.P.S.Dias and R.C.Paiva. Hopf bifurcation with S_3-symmetry, PortugaliÆ Mathematica 63 (2) (2006) 127-155. pdf

A.P.S.Dias and J.S.W.Lamb. Local bifurcation in symmetric coupled cell networks: linear theory. Physica D 223 (2006) 93-108. pdf

A.P.S.Dias and A.Rodrigues. Secondary Bifurcations in Systems with All-to-All Coupling. Part II. Dynamical Systems 21 (2006) 439-463. pdf

M.A.D.Aguiar and A.P.S.Dias. Minimal Coupled Cell Networks. Nonlinearity 20 (2007) 193-219. pdf

M.A.D.Aguiar, A.P.S.Dias, M.Golubitsky and M.C.A.Leite. Homogeneous coupled cell networks with S_3-symmetric quotient. Discrete and Continuous Dynamical Systems Supplement (2007) 1-9. pdf

F. Antoneli, A.P.S.Dias and R.C. Paiva. Hopf Bifurcation in Coupled Cell Networks with Interior Symmetries. SIAM Journal on Applied Dynamical Systems 7 (1) (2008) 220-248.pdf

F. Antoneli, A.P.S.Dias and P.C.Matthews. Invariants, Equivariants and Characters in Symmetric Bifurcation Theory. Proceedings of the Royal Society of Edinburgh 138A (2008) 477-512.pdf

M.A.D.Aguiar, A.P.S.Dias, M.Golubitsky and M.C.A.Leite. Bifurcations from regular quotient networks: A first insight Physica D 238 (2009) 137-155. pdf

F.Antoneli, P.H. Baptistelli, A.P.S.Dias and M.Manoel. Invariant Theory and Reversible-Equivariant Vector Fields. Journal of Pure and Applied Algebra 213 (2009) 649-663.pdf pdf2

A.P.S.Dias and A.Rodrigues. Hopf bifurcation with S_n symmetry. Nonlinearity 22 (2009) 627-666. pdf

A.P.S.Dias and E.M.Pinho. Spatially Periodic Patterns of Synchrony in Lattice Networks. SIAM Journal on Applied Dynamical Systems 8 (2) (2009) 641-675. pdf

A.P.S.Dias, P.C.Matthews and A.Rodrigues. Generating Functions for Hopf Bifurcation with S_n-Symmetry. Discrete and Continuous Dynamical Systems - Series A 25 (3) (2009) 823-842. pdf

A.P.S.Dias and E.M.Pinho. On the enumeration of periodic patterns of synchrony via finite bidirectional networks. Proceedings A of the Royal Society of London 466 (2010) 891-910. pdf

F.Antoneli, A.P.S.Dias and C.M.A.Pinto. Quasi-periodic States in Coupled Rings of Cells. Communications in Nonlinear Science and Numerical Simulations 15 (4) (2010) 1048-1062. pdf

Book

J.Buescu, S.B.S.D.Castro, A.P.S.Dias and I.S.Labouriau (eds). Bifurcations, symmetry and patterns. A conference in honour of M.Golubitsky and I.Stewart, Birkhauser Verlag, Basel, Switzerland, 2003. (ISBN 3-7643-7020-3)

Publication in conference proceedings (with referee)

F.Antoneli, A.P.S.Dias and C.M.A.Pinto. Rich phenomena in a network of two rings coupled through a `buffer' cell. In: Proceedings 2nd Conference on Nonlinear Science and Complexity, ISEP, July 28-31 2008, Porto, Portugal To appear. pdf

F.Antoneli, A.P.S.Dias and R.C.Paiva. Coupled Cell Networks: Hopf bifurcation and Interior Symmetry. AIMS proceedings (2011) To appear. pdf

Publications in conference proceedings (without referee)

F.Antoneli, A.P.S.Dias, M.Golubitsky and Y.Wang. Flow Invariant Subspaces for Lattice Dynamical Systems. In: Workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation in PDE. (W. Nagata and N.S. Namachchivaya, eds.) Fields Institute Communications, 2006, 1-8. pdf

F.Antoneli, A.P.S.Dias, M.Golubitsky and Y.Wang. Synchrony in Lattice Differential Equations. In: Some topics in industrial and applied mathematics. (R. Jeltsch, T. Li and I.H. Sloan, eds.) Contemporary Applied Mathematics Series 8 World Scientific Publ. Co., 2007, 43-56. pdf

M.A.D.Aguiar and A.P.S.Dias. Coupled cell networks: minimality. PAMM Proc. Appl. Math. Mech. 7 , 1030501-1030502 (2007). pdf

A.P.S.Dias and R.C. Paiva. Hopf bifurcation in coupled cell networks with abelian symmetry. In: Actas do Encontro Nacional da SPM Leiria 2010. Boletim da Sociedade Portuguesa de Matemática, 2011, 110-115. pdf

Other publication

A.P.S.Dias and E.M.Pinho. Regras de boa vizinhança. Gazeta de Matemática 162 (2010) 49-56. pdf

Abstract of communication

A.P.S.Dias, B.Dionne and I.Stewart. Heteroclinic cycles and wreath product symmetries, p.53-57. In: D.Bambusi, G.Gaeta and M.Cadoni, 2001. Proceedings of the International Conference on Symmetry and Perturbation Theory, Sardinia, Italy, 2001, World Scientific, Singapore.

Preprints

A.P.S.Dias and R.C.Paiva. A remark on Hopf bifurcation in one-dimensional symmetric coupled cell networks. Preprint 2011 pdf

A.P.S. Dias and C.S. Moreira. Spectrum of the elimination of loops and multiple arrows in coupled cell networks. CMUP Preprint 2012-9 pdf