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Random attractors for first order stochastic retarded lattice dynamical systems. (English) Zbl 1309.37076

Summary: This paper is concerned with the existence of random attractors for a general first order stochastic retarded lattice dynamical systems. It shows that, under suitable dissipative conditions, such a system possesses a random attractor which is a random compact invariant set. Furthermore, the ergodicity of the system is also proven.{
©2010 American Institute of Physics}

MSC:

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
34K31 Lattice functional-differential equations
34D45 Attractors of solutions to ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
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