37 citations · 183 across the 20 of their papers we have counts for
23 papers
Symmetry-breaking-induced loss of ergodicity in maps of the simplex with inversion symmetry
Bastien Fernandez, Eric Vernier
Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we pro…
Slow-fast dynamics in stochastic Lotka-Volterra systems
Julien Barré, Bastien Fernandez, Grégoire Panel
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On sh…
Conditioning problems for invariant sets of expanding piecewise affine mappings: Application to loss of ergodicity in globally coupled maps
Bastien Fernandez, Fanni M. Selley
We propose a systematic approach to the construction of invariant union of polytopes (IUP) in expanding piecewise affine mappings whose linear components are isotropic scalings. Th…
Computer-assisted proof of ergodicity breaking in expanding coupled maps
Bastien Fernandez
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at th…
Selective chaos of travelling waves in feedforward chains of bistable maps
Bastien Fernandez
We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the p…
The variation of invariant graphs in forced systems
Bastien Fernandez, Anthony Quas
In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primar…