Monday 17 Jun 2013: Random Attractors and the Preservation of Synchronization in the Presence of Noise
Peter Kloeden - Goethe University
Laver LT3 16:00-17:00
The long term behaviour of dissipatively synchronized deterministic systems is determined by the system with the averaged vector field of the original uncoupled systems. This effect is preserved in the presence of environmental -- i.e., background or additive -- noise provided stochastic stationary solutions are used instead of steady state solutions. Random dynamical systems and random attractors provide the appropriate mathematical framework for such problems and require Ito stochastic differential equations to be transformed into pathwise random ordinary differential equations. The effects of discretization and synchronization under lienar nosie will also be mentioned. An application to a system of semi-linear parabolic stochastic partial differential equations with additive space-time noise on the union of thin bounded tubular domains separated by a permeable membrane will be considered.