Random uniform exponential attractors for non-autonomous stochastic lattice systems and FitzHugh-Nagumo lattice systems with quasi-periodic forces and multiplicative noise

We first give an existence criterion for a random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system defined on the product space of N-weighted spaces of infinite sequences. Then, based on this criterion, we prove the existence of random uniform exponential attractors for stochastic lattice systems and stochastic FitzHugh-Nagumo lattice systems that are both with quasi-periodic forces.