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Dynamical behavior for stochastic lattice systems. (English) Zbl 1134.37350

Summary: Random attractors describe the long term behavior of the random dynamical systems. This paper is devoted to a general first order stochastic lattice dynamical systems (SLDS) with some dissipative nonlinearity. We prove the asymptotic compactness of the random dynamical system and obtain the random attractor, which is a compact random invariant set with tempered bound.

MSC:

37H99 Random dynamical systems
34F05 Ordinary differential equations and systems with randomness
37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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