Résumé : We deal with an abstract system of two coupled nonlinear
stochastic (infinite dimensional) equations subjected to additive
white noise type process. This kind of systems may describe various
interaction phenomena in a continuum random medium. Under suitable
conditions we prove the existence of an exponentially attracting
random invariant manifold for the coupled system. This
result means that under some conditions we observe (nonlinear)
synchronization phenomena in the coupled system. As applications we
consider stochastic systems consisting of (i) parabolic and
hyperbolic equations, (ii) two hyperbolic equations, and (iii)
Klein-Gordon and Schredinger equations.

Based on a joint paper with B. Schmalfuss.

Cet exposé se tiendra en salle C20-13, 20ème étage, Université
Paris 1, Centre Pierre Mendes-France, 90 rue de Tolbiac, 75013 Paris
(métro : Olympiades).