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Bastien
Fernandez
Centre
de Physique Théorique
CNRS Luminy Case 907 13288 Marseille CEDEX 09 France Tel: [+33] 491 269 549 [Bastien.Fernandez@cpt.univ-mrs.fr] |
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| Centre de Physique Théorique is supported by CNRS, Université de Provence, Université de la Méditerranée and Université de Toulon-Var. | |||||||||
| Research
interests My research interests lie in the domain of Spatially Extended Dynamical Systems. I have mainly focused on Coupled Map Lattices [CML]. CML are discrete time models for the dynamics of systems which are extended in space. They have been applied to various domains in Physics [eg. nonlinear of chains of interacting particles], in Chemistry [eg. reaction-diffusion process], in Biology [eg. population dynamics], etc. From the mathematical point of view, describing the phenomenology of a CML brings new challenges to the theory of Dynamical Systems. Another of my scientific interests is the dynamics of Fronts in Bistable Systems with Discrete Time [collaboration with R Coutinho]. We have developed a formalism that encompasses in a unique framework, spatially continuous systems and discrete lattices. In particular, this allows to describe velocity changes with the direction of motion in multidimensional lattices with arbitrary convolution coupling [Animation here]. |
| For more details on CML and Fronts,
see Dynamics of Coupled Map Lattices and of related spatially extended systems Lecture Notes in Physics 671, Springer-Verlag [2005] co-edited with J-R Chazottes. |
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My interests also concern Regulatory
Networks in
Genetic and Immunology. Regulatory networks induce models with interesting original dynamics. For more details, see math.DS/0505044 [published in J. Math. Bio. 52 (2006) 524-570] |
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| [This picture shows the basins of attraction of permanent oscillations in a negative feeback circuit with 2 genes. Courtesy by R Coutinho.] | ||
| [Picture gallery of attractor basins in negative feedback circuits] | ||
| I have studied the Metastable phenomena
occuring in Coupled Stochastic
Differential Equations in
the limit of weak noise. [collab. N
Berglund / B Gentz] [see mp_arc/06-337
and mp_arc/06-338,
published in Nonlinearity 20 (2007)] This work is part of the (former) project Stochastic modelling of non-equilibrium systems. |
| More recently, we have investigated the Route to
Synchronisation in two coupled
piecewise expanding
maps. This relied on coupling dependent estimates on the Symbolic Dynamics
(pruning) and topological entropy. [collab. R
Coutinho/P
Guiraud] |
| News |
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Spatial chaos of traveling waves has a given velocity, with B Luna and E Ugalde, Phys. Rev. E 80 (2009) 025203(R) [Preprint: hal-00411530] | |
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| Athermal dynamics of strongly coupled stochastic three-state oscillators, with L Tsimring, Phys. Rev. Lett. 100 (2008) 165705 [Preprint: hal-00265346] | ||
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Popular book Le monde des nombres Le Pommier Paris (2000). Portuguese translation: O mundo dos numeros Instituto Piaget Lisbon (2005). |
