Bifurcations of emerging patterns in the presence of additive noise

Gonzague Agez (1) , Marcel G Clerc (2) , Eric Louvergneaux (3) , René G Rojas (4)

1 CEMES - Centre d'élaboration de matériaux et d'études structurales
2 UCHILE - Universidad de Chile = University of Chile [Santiago]
3 PhLAM - Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523
4 PUCV - Pontificia Universidad Católica de Valparaíso

A universal description of the effects of additive noise on super-and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.

Domaines: Physique [physics]

Gonzague Agez, Marcel G Clerc, Eric Louvergneaux, René G Rojas. Bifurcations of emerging patterns in the presence of additive noise. Physical Review E , 2013, 87 (4), pp.042919. ⟨10.1103/PhysRevE.87.042919⟩. ⟨hal-01730533⟩