In this talk Dr. Verena Köpp from Friedrich-Schiller-University in Jena, Germany considers a system of two coupled nonlinear stochastic lattice equations driven by additive white noise processes. After a brief introduction to the theory of random dynamical systems, we study the long-term behavior of the system generated by the given equations when the intensity of the coupling gets large. In this setting we observe that the system synchronizes in a certain sense. To describe this phenomenon we prove the upper semicontinuity of the corresponding family of random attractors with respect to the random attractor of a specific limiting system.

Thanks to Professor Hakima Bessaih for hosting the speaker.