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- Renato Coutinho, Bastien Fernandez, RONDON LIMA, Arnaud Meyroneinc
- Journal of mathematical biology
- 2006

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)

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 spatiotemporal 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)

- Bastien Fernandez
- I. J. Bifurcation and Chaos
- 2008

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)

- Todd R. Young, Bastien Fernandez, Richard Buckalew, Gregory Moses, Erik M. Boczko
- Journal of theoretical biology
- 2012

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 study the interfaces’ time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts,… (More)

We consider the dynamics of a periodic chain ofN 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), the system synchronises, in the… (More)

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise. 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. The system shows a metastable behaviour, which is characterised by the location and stability of… (More)

- Alain Barrat, Bastien Fernandez, Kevin K. Lin, Lai-Sang Young
- Physical review letters
- 2013

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)

- Bastien Fernandez, Lev S. Tsimring
- Physical review. E, Statistical, nonlinear, and…
- 2011

Strongly nonlinear degrade-and-fire (DF) oscillations may emerge in genetic circuits having a delayed negative feedback loop as their core element. Here we study the synchronization of DF oscillators coupled through a common repressor field. For weak coupling, initially distinct oscillators remain desynchronized. For stronger coupling, oscillators can be… (More)