Publications

Articles in journals

  1. 1.Kink's dynamics in one-dimensional coupled map lattices, Chaos 5 (1995) 602-608, chao-dyn/9410004


  1. 2.Existence and stability of steady fronts in bistable coupled map lattices, J. Stat. Phys. 82 (1996) 931-950, patt-sol/9511001


  1. 3.The propagating fronts in a bistable CML, J. Stat. Phys. 86 (1997) 337-350, with L. Raymond


  1. 4.On the eigenvalues of some transfer matrices, J. Comp. Appl. Math. 81 (1997) 249-255, with M. Pindor


  1. 5.Extended symbolic dynamics in bistable CML: Existence and stability of fronts, Physica D 108 (1997) 60-80, with R. Coutinho, patt-sol/9609004


  1. 6.On the global orbits in a bistable CML, Chaos 7 (1997) 301-310, with R. Coutinho


  1. 7.Fronts and interfaces in bistable extended mappings, Nonlinearity 11 (1998) 1407-1433, with R. Coutinho,  patt-sol/9805006


  1. 8.Population dynamics in heterogeneous environments, Int. J. Bif. & Chaos 10 (2000) 1993-2000, with V. Tereshko,  [Comments and corrections: .pdf]


  1. 9.Topological properties of linearly coupled expanding map lattices, Nonlinearity 13 (2000) 973-993, with V. Afraimovich [Erratum: errataf00.pdf]


  1. 10.On the stability of periodic orbits in lattice dynamical systems, Dynamical Systems 16 (2001) 247-252, with A. Morante.


  1. 11.From synchronisation to multistability in two coupled quadratic maps, Phys. Lett. A 285 (2001) 327-338, with R. Carvalho and R. Vilela Mendes, nlin.CD/0005053


  1. 12.Spectrum of dimension for Poincaré recurrences of Markov maps, Discrete & Cont. Dynam. Sys. A 8 (2002) 835-849, with E. Ugalde and J. Urias.


  1. 13.Coupling two unimodal maps of simple kneading sequences, Ergod. Th. & Dynam. Sys. 24 (2004) 107-125, with M. Jiang, mp_arc/00-387


  1. 14.Route to chaotic synchronisation in coupled map lattices: rigorous results, Discrete & Cont. Dynam. Sys. B 4 (2004) 435-455, with P. Guiraud, nlin.CD/0210019


  1. 15.Fronts in extended systems of bistable maps coupled via convolutions, Nonlinearity 17 (2004) 23-47, with R. Coutinho, .pdf


  1. 16.Spatially extended circle maps: Monotone periodic dynamics of functions with linear growth, J. Nonlinear Sci. 14 (2004) 93-118, with R. Coutinho, .pdf


  1. 17.Discrete time piecewise affine models of genetic regulatory networks, J. Math. Bio. 52 (2006) 524-570, with R. Coutinho, R. Lima and A. Meyroneinc, math.DS/0505044


  1. 18.Metastability in interacting nonlinear stochastic differential equations I: From weak coupling to synchronisation, Nonlinearity 20 (2007) 2551-2581, with N. Berglund and B. Gentz, mp_arc/06-337


  1. 19.Metastability in interacting nonlinear stochastic differential equations II: Large-N behaviour, Nonlinearity 20 (2007) 2583-2614, with N. Berglund and B. Gentz, mp_arc/06-338


  1. 20.Symbolic dynamics of two coupled Lorenz maps: from uncoupled regime to synchronisation, Physica D 237 (2008) 2444-2462, with R. Coutinho and P. Guiraud, mp_arc/07-170


  1. 21.Global synchronisation in translation invariant coupled map lattices, Int. J. Bif. & Chaos 18 (2008) 3455-59


  1. 22.Athermal dynamics of strongly coupled stochastic three-state oscillators, Phys. Rev. Lett. 100 (2008) 165705, with L. Tsimring, hal-00265346


  1. 23.Spatial chaos of traveling waves has a given velocity, Phys. Rev. E 80 (2009) 025203(R), with B. Luna and E. Ugalde, hal-00411530 [Erratum: Phys. Rev. E 83 (2011) 039906(E)]


  1. 24.T-cell receptor (TCR) Beta allelic exclusion in dynamical models of V(D)J recombination based on allelic independence, J. Immunol. 185 (2010) 1622-32, with E. Farcot, M. Bonnet, S. Jaeger, S. Spicuglia and P. Ferrier


  1. 25.Extensive escape rate in lattices of weakly coupled expanding maps, Discrete & Cont. Dynam. Sys. A 31 (2011) 669-84, with J-B. Bardet, hal-00495616


  1. 26.Statistical properties of synchronization graphs in discontinuous forced systems, Nonlinearity 24 (2011) 2477-88, with A. Quas, hal-00562489


  1. 27.Co-repressive interaction and clustering of degrade-and-fire oscillators, Phys. Rev. E 84 (2011) 051916, with L. Tsimring, hal-00576106 [Erratum: Phys. Rev. E 90 (2014) 049901]


  1. 28.Discontinuous generalized synchronization of chaos, Dynamical Systems, 27 (2012) 105-16, hal-00562485


  1. 29.Clustering in cell cycle dynamics with general response/signaling feedback, J. Theo. Bio. 292 (2012) 103-15, with T. Young, R. Buckalew, G. Moses and E. Boczko, hal-00803131


  1. 30.Extensive bounds on the entropy of repellers in expanding coupled map lattices, Ergod. Th. & Dynam. Sys. 33 (2013) 870-95, with R. Coutinho, hal-00612623


  1. 31.Fronts between periodic patterns for bistable recursions on lattices, J. Dynam. Diff. Eq. 25 (2013) 17-31, with R. Coutinho, hal-00660246


  1. 32.Epigenetic aspects of lymphocyte antigen receptor gene rearrangement, Immunology 139 (2013) 141-50, with S. Jaeger and P. Ferrier


  1. 33.Modeling temporal networks using random itineraries, Phys. Rev. Lett. 110 (2013) 158702, with A. Barrat, K. K. Lin and L-S. Young, hal-00803124


  1. 34.Breaking of ergodicity in expanding systems of globally coupled piecewise affine circle maps, J. Stat. Phys. 154 (2014) 999-1029, hal-00903237


  1. 35.Typical trajectories of coupled degrade-and-fire oscillators: From dispersed populations to massive clustering, J. Math. Bio. 68 (2014) 1627-1652, with L. Tsimring, hal-00687741


  1. 36.Escape rate and singular limiting distributions for intermittent maps with holes, Trans. Amer. Math. Soc. 368 (2016) 4907-4932, with M.F. Demers, hal-00903238


  1. 37.Landau damping in the Kuramoto model, Ann. H. Poincaré 17 (2016) 1793-1823, with D. Gérard-Varet and G. Giacomin, arXiv:1410.6006


  1. 38.Wave generation in unidirectional chains of idealized neural oscillators, J. Math. Neurosci. (2016) 6:5, with S.M. Mintchev, arXiv:1412.0812


  1. 39.Asymptotic periodicity in networks of degrade-and-fire oscillators, Physica D 323-324 (2016) 49-56, with A. Blumenthal, arXiv:1502.06088


  1. 40.Population dynamics of globally coupled degrade-and-fire oscillators, J. Dynam. Diff. Eq. 29 (2017) 523-47, with A. Blumenthal, hal-00986128


  1. 41.Landau damping to partially locked states in the Kuramoto model, Comm. Pure Appl. Math. 71 (2018) 953-993, with H. Dietert and D. Gérard-Varet, arXiv:1606.04470


  1. 42.The total variation of invariant graphs in forced systems, Chaos 28 (2018) 083101, with A. Quas, arXiv:1802.06364


  1. 43.Revisiting asymptotic periodicity in networks of degrade-and-fire oscillators, Eur. J. Phys. ST 227 (2018) 1267-79, arXiv:1809.03228


  1. 44.The mathematics of asymptotic stability in the Kuramoto model, Proc. Roy. Soc. A 474 (2018) 0467, with H. Dietert, arXiv:1801.01309


  1. 45.Computer-assisted proof of loss of ergodicity by symmetry breaking in expanding coupled maps, Ann. H. Poincaré 21 (2020) 649-674, arXiv:1903.04941


  1. 46.Conditioning problems for invariant sets of expanding piecewise affine mappings: application to loss of ergodicity in globally coupled maps, Nonlinearity 35 (2022) 3991-4042, with F. Selley, arXiv:2008.04566


  1. 47.Slow-fast dynamics in stochastic Lotka-Volterra systems, to appear in Ann. Inst. Henri Poincaré Probab. Stat., with J. Barré and G. Panel, arXiv:2205.04370


  1. 48.Symmetry-breaking-induced loss of ergodicity in maps of the simplex with inversion symmetry, submitted, with E. Vernier, arXiv:2211.11078


  1. 49.Dynamics of buyer populations in fresh product markets, J. Nonlinear Sci. 34 (2024) 92, with A. Ellouze, arXiv:2311.03987


  1. 50.Feedback-delay dependence of the stability of cluster periodic orbits in populations of degrade-and-fire oscillators with common activator, submitted, with M. Tanzi, arXiv:2405.07752

Proceedings & chapters in books

  1. 1.The stability of periodic orbits in lattice dynamical systems, Aportaciones Matematicas 27 (2000) 115-118, with A. Morante


  1. 2.Directional entropy in lattice dynamical systems, Progress in Nonlinear Science Vol 1, Institute of Applied Physics, Niznhy Novgorod (2002) 9-30, with V. Afraimovich, M. Courbage and A. Morante


  1. 3.Un modèle d’applications couplées pour la dynamique des réseaux de régulation génétique, Compte-rendus de la 7ième rencontre du Nonlinéaire (2004) 203–208, with R. Coutinho, R. Lima and A. Meyroneinc


  1. 4.Iterative construction of fronts in bistable extended systems, Iteration theory (ECIT'02) Grazer Math. Ber. 346 (2004) 91-97, with R. Coutinho,


  1. 5.The CML2004 project, Dynamics of Coupled Map Lattices and related spatially extended systems, Lecture Notes in Physics 671, Springer-Verlag (2005), with J-R. Chazottes,  .pdf


  1. 6.Spatially extended monotone mappings, Dynamics of Coupled Map Lattices and of related spatially extended systems, Lecture Notes in Physics 671, Springer-Verlag (2005), with R. Coutinho,  .pdf


  1. 7.Route vers la synchronisation dans les réseaux d'applications chaotiques couplées, Actes du 5ième colloque sur le Chaos Temporel et Chaos Spatio-temporel, Le Havre (2005), with P. Guiraud and R. Coutinho, .pdf


  1. 8.Extensive clustering in populations of degrade-and-fire oscillators, Compte-rendus de la 15ième rencontre du Nonlinéaire (2012), with L. Tsimring


  1. 9.Selective chaos of travelling waves in feedforward chains of bistable maps, The many facets of complexity sciences, Nonlinear Physical Science, Springer (2021), arXiv:1811.08310

Book edition

  1. 1.Dynamics of Coupled Map Lattices and related spatially extended systems, Lecture Notes in Physics 671, Springer-Verlag (2005), with J-R. Chazottes

Popular book

  1. 1.Le Monde des Nombres, Le Pommier, Paris (2000). Portuguese translation “O Mundo dos Numeros”, Instituto Piaget, Lisbon (2005,2009).

V. Hirbec

V. Hirbec

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