Long term behavior of stochastic discrete complex Ginzburg-Landau equations with time delays in weighted spaces.

In this paper, we investigate the long term behavior of the solutions to a class of stochastic discrete complex Ginzburg-Landau equations with time-varying delays and driven by multiplicative white noise. We first prove the existence and uniqueness of random attractor in a weighted space for these equations. Then, we analyze the upper semicontinuity of the random attractors as the time delay approaches to zero. [ABSTRACT FROM AUTHOR]