Bastien Fernandez

Landau damping in the Kuramoto model

We consider the Kuramoto model of globally coupled phase oscillators in its continuum limit, with individual frequencies drawn from a distribution with density of class

Epigenetic aspects of lymphocyte antigen receptor gene rearrangement or ‘when stochasticity completes randomness’

{C^n}

Typical trajectories of coupled degrade-and-fire oscillators: from dispersed populations to massive clustering

Cn (

Statistical properties of invariant graphs in piecewise affine discontinuous forced systems

{n\geq 4}

On the stability of periodic orbits in lattice dynamical systems

n≥4). A criterion for linear stability of the uniform stationary state is established which, for basic examples in the literature, is equivalent to the standard condition on the coupling strength. We prove that, under this criterion, the Kuramoto order parameter, when evolved under the full nonlinear dynamics, asymptotically vanishes (with polynomial rate n) for every trajectory issued from a sufficiently small