LAUSR

In this paper, we study the existence of pullback attractors and pullback exponential attractors for lattice dynamical system in time-dependent sequence space. First, we introduce a new sequence space with time-dependent variable exponents. Second, two abstract criteria (or sufficient conditions) about the existence of pullback attractors and pullback exponential attractors are established for infinite dimensional lattice dynamical systems on time-dependent spaces of infinite sequences. Finally, for making full use of the above-mentioned abstract criteria, we consider a second order lattice system with nonstandard growth nonlinearity, and then the existence of bi-space pullback attractors and pullback exponential attractors on a time-dependent Musielak–Orlicz space is obtained. In particular, we point out that these criteria and analytical skills can be utilized to deal with other lattice systems satisfying nonstandard growth conditions.