last update 10/II/2026
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B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
Qualitative planar dynamics with star nodes and homogeneous nonlinearities: beyond Hilbert's 16th problem preprint
CMUP n. 2021-10
- arXiv: 2106.07516v7 [math.DS]
to appear in Matemática Contemporânea
B.F.F. Gonçalves, I.S. Labouriau, A.A.P. Rodrigues
Synchrony and canards in two coupled FitzHugh--Nagumo equations
Physica D 482 134853 (2025) linkpdf preprint CMUP n. 2025-6
arXiv: 2503.12596v3 [math.DS]
DOI 10.1016/j.physd.2025.134853
I.S. Labouriau, A.A.P. Rodrigues
Transitions of bifurcation diagrams of a forced heteroclinic cycle
Journal of Mathematical Analysis and Applications 546 (2) 129223 (2025)
preprint CMUP n. 2023-37
arXiv: 2312.00729v3 [math.DS]
DOI 10.1016/j.jmaa.2025.129223
B.F.F. Gonçalves, I.S. Labouriau, A.A.P. Rodrigues
Bifurcations and canards in the FitzHugh-Nagumo system: a tutorial in fast-slow dynamics
International Journal of Bifurcation and Chaos preprint CMUP n. 2024.64
arXiv: 2411.11209v2 [math.DS]
DOI: 10.1142/S0218127425300174
I.S. Labouriau, A.A.P. Rodrigues
High frequency forcing of an attracting heteroclinic network
Portugaliae Mathematica 82 (1/2) 113-137 (2025) pdf preprint
CMUP n. 2021-9 May2021
arXiv: 2306.09936v2 [math.DS]
DOI 10.4171/PM/2128
B.Alarcón, S.B.S.D. Castro, I.S. Labouriau
Global planar dynamics with a star node and contracting nonlinearity
Research in the Mathematical Sciences 11-24 (2024)
pdf preprint
CMUP n. 2023-23
arXiv: 2307.16020v2 [math.DS]
DOI 10.1007/s40687-024-00427-0
S.B.S.D. Castro, A.M.J. Ferreira, I.S. Labouriau
Stability of cycles and survival in a Jungle Game with four species
Dynamical Systems an International Journal (2024)
linkpdf preprint
CMUP n. 2023-22
arXiv: 2306.09880v2 [math.DS]
DOI 10.1080/14698367.2024.2307515
I.S. Labouriau, A.A.P. Rodrigues
Periodic forcing of a heteroclinic network
preprint arXiv: 2105.10757v3 [math.DS]
Journal of Dynamics and Differential Equations 35 (2023) 2951-2969
link
DOI 10.1007/s10884-021-10054-w
S.B.S.D. Castro, A.M.J. Ferreira, L. Garrido-da-Silva, I.S. Labouriau
Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock
SIAM Journal of Applied Dynamical Systems 21 (4) 2393-2431 (2022)
preprint
CMUP n. 2021-11 July 2021 arXiv: 2107.09383v1 [math.DS]
DOI 10.1137/21M1435215
I. S. Labouriau, E. Sovrano
Chaos in periodically forced reversible vector fields
link
Journal of Singularities 22 (2020) 227-240
DOI 10.5427/jsing.2020.22p
P. H. Baptistelli, I. S. Labouriau, M. Manoel
Recognition of symmetries in reversible maps
Journal of Mathematical Analysis and Applications 491-2 (2020) preprint
arXiv:1812.08727[math.DS]
DOI 10.1016/j.jmaa.2020.124348
I.S. Labouriau, A.A.P. Rodrigues
Bifurcations from an attracting heteroclinic cycle under periodic forcing
preprint
arXiv: 1809.04006v2 [math.DS]
Journal of Differential Equations 269 (2020) 4137-4174
DOI 10.1016/j.jde.2020.03.024
O. Podvigina, S.B.S.D. Castro, I.S. Labouriau
Asymptotic stability of robust heteroclinic networks
preprint
arXiv: 1905.06419 [math.DS]
Nonlinearity 33-4 (2020) 1757-1788
DOI 10.1088/1361-6544/ab6817
O. Podvigina, S.B.S.D. Castro, I.S. Labouriau
Stability of a heteroclinic network and its cycles:
a case study from Boussinesq convection
preprint
- arXiv: 1712.04270v2 [math.DS]
Dynamical Systems an International Journal 34-1 (2019) 157-193
DOI 10.1080/14689367.2018.1486807
S.B.S.D. Castro, I.S. Labouriau, J.F. Oliveira
Projections of patterns and mode interactions preprint - arXiv: 1703.10635v4 [math.DS]
Dynamical Systems an International Journal 33-4 (2018) 547-564
link
- published online 5 dec 2017
DOI: 10.1080/14689367.2017.14014590
I.S. Labouriau, E.M.O. Pinho
Periodic Functions, Lattices and Their Projections preprint
CMUP n. 2018-11 September 2018 - arXiv: 1809.07298 [math.DS]
B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
Global Saddles for Planar Maps
preprint
- arXiv: 1605.08000v2 [math.DS]
Journal of Dynamics and Differential Equations 30 (2) (2018) 601-612
DOI: 10.1007/s10884-016-9561-3 read-only link
I.S. Labouriau, A.A.P. Rodrigues
On Takens' Last Problem:
tangencies and time averages near heteroclinic networks preprint
- arXiv: 1606.07017v2 [math.DS]
Nonlinearity 30 (2017) 1876-1910
DOI: 10.1088/1361-6544/aa64e9
I.S. Labouriau, A.A.P. Rodrigues
Global bifurcations close to symmetry
preprint
arXiv: 1504.01659 [math.DS]
Journal of Mathematical Analysis and Applications 444-1 (2016) 648-671
DOI: 10.1016/j.jmaa.2016.06.032
I.S. Labouriau, A.C. Murza
Limit cycles for a class of Z_2n-equivariant systems without infinite equilibria preprint
arXiv:1510.00853v2 [math.DS]
Electronic Journal of Differential Equations vol 2016 (2016) no. 122 pp 1-12
pdf
I.S. Labouriau, A.C. Murza
Hopf bifurcation with tetrahedral and octahedral symmetry
preprint
arXiv:1407.2866v2
SIAM Journal of Applied Dynamical Systems 15-1 (2016) 106-124
DOI: 10.1137/15M1009317
I.S. Labouriau, A.A.P. Rodrigues
Dense heteroclinic tangencies near a Bykov cycle
Journal of Differential Equations 259 (2015) 5875-5902
preprint
- arXiv: 1402.5455 link
DOI: 10.1016/j.jde.2015.07.017
B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
Discrete Symmetric Planar Dynamics
preprint
in J.-P. Bourguignon, R. Jeltsch, A.A. Pinto, M. Viana (eds),
Dynamics, Games and Science;
CIM Series in Mathematical Sciences, Springer-Verlag (2015) 17-30
DOI 10.1007/978-3-319-16118-1_2
A.A.P. Rodrigues, I.S. Labouriau
Spiralling dynamics near heteroclinic networks
Physica D 268 (2014) 34-39 preprint - arXiv:1304.5283
DOI: 10.1016/j.physd2013.10.012
E.M.O. Pinho, I.S. Labouriau
On the projection of functions invariant under the action of a crystallographic group
Journal of Pure and Applied Algebra 218 (2014) 37-51
preprint
DOI:10.1016/j.jpaa.2013.04.010
M.J. Álvarez, I.S. Labouriau, A.C. Murza
Limit cycles for a class of quintic Z_6-equivariant systems without infinite critical points
preprint - arXiv:1309.5346
Bulletin of the Belgian Mathematical Society - Simon Stevin 21 (2014) 841-857
I.S. Labouriau, A.C. Murza
Periodic solutions in an array of coupled FitzHugh-Nagumo cells
preprint - arXiv:1304.0027
Journal of Mathematical Analysis and Applications 412 (2014) 29-40
DOI:10.1016/j.jmaa.2013.10.041
B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
Global Dynamics for Symmetric Planar Maps
Discrete and Continuous Dynamical Systems series A 33:8 (2013) 2241-2251
preprint
DOI: 10.3934/dcds.2013.33.2241
I.S. Labouriau, A.A.P. Rodrigues
Partial symmetry breaking and heteroclinic tangencies
preprint - arXiv:0654849
in S. Ibáñez, J.S. Pérez del Río, A. Pumariño and J.A. Rodríguez (eds),
Progress and challenges in dynamical systems (2013) 281-299 Springer Proceedings in Mathematics and Statistics
I.S. Labouriau, A.A.P. Rodrigues
Global Generic Dynamics Close to Symmetry
Journal of Differential Equations 253:8 (2012) 2527-2557
linkpreprint
DOI: 10.1016/j.jde.2012.06.009
B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
A local but not global attractor for a $\Z_n$-symmetric map
Journal of Singularities 6 (2012) 1-14
preprint
DOI: 10.5427/jsing.2012.6a
B. Alarcón, S.B.S.D. Castro, I.S. Labouriau
The discrete Markus-Yamabe problem for symmetric planar polynomial maps
Indagationes Mathematicae 23 (2012) 603-608
preprint
DOI: 10.1016/j.indag.2012.06.001
A.A.P. Rodrigues, I.S. Labouriau, M.A.D. Aguiar
Chaotic double cycling
Dynamical Systems an International Journal 26:2 (2011) 199-233
DOI: 10.1080/1489367.2011.557179
P.R.F. Pinto, M.S. Baptista and I.S. Labouriau
Density of first Poincaré returns, periodic orbits and Kolmogorov-Sinai entropy
Communications in Nonlinear Science and Numerical Simulations, 16-2 (2011) 863-875
DOI: 10.1016/j.cnsns.2010.05.018
S.B.S.D. Castro , I.S. Labouriau, O. Podvigina
A heteroclinic network in mode interaction with symmetry
Dynamical Systems an International Journal 25-3 (2010) 359-396
DOI: 10.1080/14689367.2010.506183
I.S.Labouriau and P.R.F. Pinto,
The geometry of Hopf and saddle-node bifurcations for waves of Hodgkin-Huxley type,
in "Real and Complex Singularities",
C.T.C. Wall, M.C. Romero-Fuster, M.G. Manoel (eds.)
London Mathematical Society Lecture Notes 380 (2010) 229-245
DOI: 10.1017/CBO9780511731983.018
M.A.D. Aguiar, I.S. Labouriau and A.A.P. Rodrigues
Switching near a network of rotating nodes
Dynamical Systems an International Journal, 25-1 (2010) 75-95
DOI: 10.1080/14689360903252119
E.M.O. Pinho and I.S. Labouriau
Symmetries of projected symmetric patterns
Preprint CMUP n. 2007-4 January 2007
pdf
M.A.D. Aguiar, S.B.S.D. Castro and I.S. Labouriau
Simple vector fields with complex behaviour
International Journal of Bifurcation and Chaos, 16-2 (2006) 369-381
I.S. Labouriau and E. M. O. Pinho,
Symmetries of projected wallpaper patterns,
Mathematical Proceedings of the Cambridge Phylosophical Society, 141 (2006) 421-441
I.S. Labouriau and M.A.S. Ruas,
Invariants for Bifurcation
Houston Journal of Mathematics, 32-2 (2006) 445-458
pdf
I.S. Labouriau and E.M.O. Pinho
Projected wallpaper patterns,
in
Brasselet, J-P; Ruas, M.A.S. (Eds.),
Real and Complex Singularities ---- São Carlos Workshop 2004
Birkhauser, Series: Trends in Mathematics (2006) 209-217
S.M.C. Abreu, I.S.Labouriau and S.B.S.D. Castro,
Construction of Symmetric Heteroclinic Cycles,
Preprint CMUP n. 2006-16 April 2006 pdf
C.M.A. Pinto, I.S. Labouriau,
Two coupled neurons pdf
in 2006 IEEE International Conference on Computational Cybernetics, ICCC
M.A.D. Aguiar, S.B.S.D. Castro and I.S. Labouriau
Dynamics near a heteroclinic network,
Nonlinearity, 18 (2005) 391-414
M.A.D. Aguiar, S.B.S.D. Castro and I.S. Labouriau
Switching along a network,
"Proceedings Equadiff 2003" F. Dumortier, H. Broer, J.Mawhin, A. Vanderbauwhede, S. Lunel(eds.)
World Scientific, (2005). 449-451
I.S.Labouriau and C.M.S.G. Rito
Stability of equilibria in equations of Hodgkin-Huxley type,
Contemporary Mathematics, vol 354 (2004) 137-143
I.S. Labouriau and C.M.A.Pinto
Loss of Synchronization in Partially Coupled Hodgkin-Huxley Equations,
Bulletin of Mathematical Biology, 66 (2004), 539-557
I.S. Labouriau and H. M. Rodrigues,
Synchronization of Coupled Equations of Hodgkin-Huxley Type,
Dynamics of Continuous, Discrete and Impulsive Systems
Series A: Mathematical Analysis 10 (2003) 463-476
I.S. Labouriau and C.M. Alves-Pinto,
Bifurcations in symmetrically coupled Hodgkin-Huxley equations,
Preprint - CMUP n. 2003-16, June 2003 pdf
M.A.D. Aguiar, S.B.S.D.Castro and I.S. Labouriau,
Path formulation for a modal family,
Portugaliae Mathematica, 58-4 (2001) 407-424
M.G.M. Gomes, I.S. Labouriau and E.M. Pinho,
Spatial Hidden Symmetries in Pattern Formation in
"Pattern Formation in Continuous and Coupled Systems",
M. Golubitsiky, D. Luss, S.H. Strogatz (eds.), Springer-Verlag, 2001
DOI: 10.1007/978-1-4612-1558-5_7
S.Castro and I.S. Labouriau,
Counting Persistent Pitchforks,
in "V International Workshop on Real and Complex Singularities" , São Carlos, Brasil,
W.Bruce and F. Tari (eds.), Research notes of the CRC Press, (2000) 215-222
L.G. Labouriau and I.S. Labouriau,
An extension of the absolute reaction rate theory as applied to
physiological rate processes,
Ciência and Cultura 49-3 (1997) 177-189
Hodgkin-Huxley system pdf
Action potential pdf
Entries in Encyclopaedia of Mathematics, Kluwer, 1997
I.S. Labouriau and M.A.S. Ruas,
Singularities of equations of Hodgkin-Huxley type,
Dynamical Systems an International Journal (formerly Dynamics and Stability of Systems), 11-2 (1996) 91-108
DOI: 10.1080/02681119608806218
I.S. Labouriau and A.P. Dias,
Instant chaos is chaos in slow motion,
Journal of Mathematical Analysis and Applications 199-2 (1996) 138-148
DOI: 10.1006/jmaa.1996.0131
J. Guckenheimer and I.S. Labouriau,
Bifurcation of the Hodgkin and Huxley equations: a new twist,
Bulletin of Mathematical Biology 55-5 (1993) 937-952
DOI: 10.1007/BF02460693
L.G. Labouriau and I.S. Labouriau,
The Arrhenius plot of a physiological rate process is never linear,
Ciência and Cultura 43-5 (1991) 363-369
W.W.Farr, Chengzhi Li, I.S. Labouriau and W.F.Langford,
Degenerate Hopf bifurcation formulas and Hilbert's 16th problem,
SIAM J. of Mathematical Analysis, 20-1 (1989) 13-30
DOI: 10.1137/0520002
I.S. Labouriau,
Degenerate Hopf bifurcation and nerve impulse, Part II,
SIAM J. of Mathematical Analysis, 20-1 (1989) 1-12
DOI: 10.1137/0520001
I.S. Labouriau,
Note on the unfolding of degenerate Hopf bifurcation germs,
J. of Differential Equations 57 (1985) 436-439
DOI: 10.1016/0022-0396(85)90064-6
I.S. Labouriau,
Degenerate Hopf bifurcation and nerve impulse,
SIAM J. of Mathematical Analysis 16 (1985) 1121-1133
DOI: 10.1137/0516083
