SLOW MANIFOLD AND PARAMETER ESTIMATION FOR A NONLOCAL FAST-SLOW DYNAMICAL SYSTEM WITH BROWNIAN MOTION  

作　　者：Hina ZULFIQAR Ziying HE Meihua YANG Jinqiao DUAN Hina ZULFIQAR;贺紫盈;杨美华;段金桥(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;Center for Mathematical Sciences,Huazhong University of Science and Technology,Wuhan 430074,China;School of Science,Wuhan University of Technology,Wuhan 430074,China;Department of Applied Mathematics,Illinois Institute of Technology,Chicago,IL 60616,USA)

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]Center for Mathematical Sciences,Huazhong University of Science and Technology,Wuhan 430074,China [3]School of Science,Wuhan University of Technology,Wuhan 430074,China [4]Department of Applied Mathematics,Illinois Institute of Technology,Chicago,IL 60616,USA

出　　处：《Acta Mathematica Scientia》2021年第4期1057-1080,共24页数学物理学报（B辑英文版）

基　　金：supported by NSF (1620449);NSFC (11531006 and 11771449)

摘　　要：We establish a slow manifold for a fast-slow dynamical system with anomalous diffusion,where both fast and slow components are influenced by white noise.Furthermore,we verify the exponential tracking property for the established random slow manifold,which leads to a lower dimensional reduced system.Alongside this we consider a parameter estimation method for a nonlocal fast-slow stochastic dynamical system,where only the slow component is observable.In terms of quantifying parameters in stochastic evolutionary systems,the provided method offers the advantage of dimension reduction.

关 键 词：Nonlocal Laplax:ian fast-slow system stochastic system random slow manifold exponential tracking property parameter estimation 

分 类 号：O19[理学—数学]