On the forward dynamical behaviour of nonautonomous lattice dynamical systems
On the forward dynamical behaviour of nonautonomous lattice dynamical systems
复制标题
非自治晶格动力系统的正向动力行为
DOI：
10.1080/10236198.2021.1962850
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Jintao Wang
中科院分区：
文献类型：
--
作者：
Chunqiu Li;Jintao Wang
本文研究了非自治格点系统的正向动力学行为。我们首先在由一般非自治格点系统生成的斜积流的全局吸引子的任意小邻域中构造一族集合{A（Σ）（sigma）}（sigma是Sigma的元素），它是前向不变的，并且一致前向吸引相空间的任何有界子集.此外，在适当的条件下，我们进一步构造了一个集合族{B-Sigma（sigma）}（sigma是Sigma的一个元素），使得它一致向前指数吸引相空间的有界子集.作为应用，我们详细研究了离散的Gray-Scott模型，并举例说明了如何将我们的抽象结果应用到具体的格系统中。
In this article, we study the forward dynamical behaviour of nonautonomous lattice systems. We first construct a family of sets {A(epsilon)(sigma)}(sigma is an element of Sigma) in the arbitrary small neighbourhood 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 {B-epsilon(sigma)}(sigma is an element of Sigma) 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.