Abstract
In this paper, we study the asymptotic behavior of stochastic discrete complex non-autonomous Ginzburg-Landau equations with multiplicative noise. We prove the existence and uniqueness of the random attractor.
Highlights
Spatially discrete systems have drawn considerable attention, especially in the study of biological systems, atomic chains, solid state physics, electrical lattices, and BoseEinstein condensates
The different dynamical behavior of spatially discrete systems has been studied in many works, such as [ – ] for traveling waves solutions, [ – ] for chaos behavior and [ – ] for global attractors
The discrete complex GinzburgLandau equation is encountered in several diverse branches of physics, ranging from superconductivity and nonlinear optics, to Bose-Einstein condensates
Summary
Spatially discrete systems have drawn considerable attention, especially in the study of biological systems, atomic chains, solid state physics, electrical lattices, and BoseEinstein condensates. The existence of random attractors for non-autonomous random dynamical systems was first proved in [ ] and in [ – ]. To the best of our knowledge, there are no results on the existence of random attractors for stochastic discrete complex non-autonomous Ginzburg-Landau equation with multiplicative noise.
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