2021/03/09 by Li, Chunqiu, Wang, Jintao
#35B40 #35B41 #35Q92 #37L50 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.05268
In this article, we study the forward dynamical behavior of nonautonomous lattice systems. We first construct a family of sets \Aε(σ)\σ∈ Σ in arbitrary small neighborhood of a global attractor of the skew-product flow generated by a general nonautonomous lattice system, which is forward invariant and uniformly forward attracts any bounded subset of the phase space. Moreover, under some suitable conditions, we further construct a family of sets \Bε(σ)\σ∈ Σ such that it uniformly forward exponentially attracts bounded subsets of the phase space. As an application, we study the discrete Gray-Scott model in detail and illustrate how to apply our abstract results to some concrete lattice system.