Dynamics of non-autonomous stochastic second order lattice systems

For non-autonomous lattice dynamical systems, extensive research has been conducted on the existence of uniform and pullback attractors in deterministic cases, and the existence of random pullback attractors in stochastic frameworks. However, these random pullback attractors do not adequately describe forward dynamics. In this work, we carefully investigate the existence of the random uniform attractor for a class of non-autonomous stochastic second-order lattice dynamical systems influenced by multiplicative white noise, which characterizes forward dynamics through uniform forward attraction in a probabilistic sense and provides new insights into the asymptotic behavior of such systems.