数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 523-537.

• 论文 • 上一篇    下一篇

离散的三分量可逆Gray-Scott模型的不变Borel概率测度

肖巧懿(),李春秋*()   

  1. 温州大学数学系 浙江温州 325035
  • 收稿日期:2019-11-03 出版日期:2021-04-26 发布日期:2021-04-29
  • 通讯作者: 李春秋 E-mail:xiaoqiaoyi1127@139.com;licqmath@tju.edu.cn
  • 作者简介:肖巧懿, E-mail: xiaoqiaoyi1127@139.com
  • 基金资助:
    国家自然科学基金(11871368)

Invariant Borel Probability Measures for the Discrete Three Component Reversible Gray-Scott Model

Qiaoyi Xiao(),Chunqiu Li*()   

  1. Department of Mathematics, Wenzhou University, Zhejiang Wenzhou 325035
  • Received:2019-11-03 Online:2021-04-26 Published:2021-04-29
  • Contact: Chunqiu Li E-mail:xiaoqiaoyi1127@139.com;licqmath@tju.edu.cn
  • Supported by:
    the NSFC(11871368)

摘要:

研究由非自治三分量可逆Gray-Scott模型在无穷格点上所生成过程的相关时均观测的Borel概率测度.首先,证明该过程存在拉回-$ {\cal D} $吸引子.进一步,建立由该拉回吸引子所支撑的唯一一族不变Borel概率测度的存在性.

关键词: 不变测度, 格点动力系统, 拉回吸引子, 非自治Gray-Scott模型

Abstract:

In this paper, we study the Borel probability measures that can be associated to the time averaged observation of the process generated by the nonautonomous three component reversible Gray-Scott model on infinite lattices. We first show that there exists a pullback-$ {\cal D} $ attractor for the process. Furthermore, we establish the existence of a unique family of invariant Borel probability measures carried by this pullback attractor.

Key words: Invariant measures, Lattice dynamical system, Pullback attractor, Nonautonomous Gray-Scott model

中图分类号: 

  • O192