Random attractor for second-order stochastic delay lattice sine-Gordon equation

Abstract

Abstract In this paper, we prove the existence of random D $\mathcal{D}$ -attractor for the second-order stochastic delay sine-Gordon equation on infinite lattice with certain dissipative conditions, and then establish the upper bound of Kolmogorov ε-entropy for the random D $\mathcal{D}$ -attractor.

Keywords

• Stochastic lattice dynamical systems
• Asymptotically compact
• Random attractor
• Kolmogorov ε-entropy