Bastien Fernandez

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We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N 2), the system synchronises, in the(More)
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. These models reduce to boolean networks in one limiting case of a parameter, and their(More)
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Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and(More)
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one correspondence between the set of global orbits and the set of admissible codes. This relationship is applied to the study of the (uniform) fronts' dynamics. It is(More)
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an admissibility condition, approximations of the corresponding symbolic systems are obtained. These approximations imply(More)
We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our construction uses random walks of variable length to produce time-extended structures with adjustable features. The procedure is(More)
A sufficient condition for global synchronization in coupled map lattices (CML) with translation invariant coupling and arbitrary individual map is proved. As in [Jost & Joy, 2001] where CML with reflection invariant couplings are considered, the condition only involves the linearized dynamics in the diagonal, namely for all points in the diagonal, the(More)