离散的三分量可逆Gray-Scott模型的不变Borel概率测度

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

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-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.

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-D attractor for the process.Furthermore,we establish the existence of a unique family of invariant Borel probability measures carried by this pullback attractor.