数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1057-1080.doi: 10.1007/s10473-021-0403-y

• 论文 • 上一篇    下一篇

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

Hina ZULFIQAR1, 贺紫盈2, 杨美华3, 段金桥4   

  1. 1. 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;
    2. School of Science, Wuhan University of Technology, Wuhan 430074, China Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China;
    3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    4. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2019-11-18 修回日期:2020-04-24 出版日期:2021-08-25 发布日期:2021-09-01
  • 作者简介:Hina ZULFIQAR,E-mail:hinazulfiqar@hust.edu.cn;Ziying HE,E-mail:ziyinghe@whut.edu.cn;Meihua YANG,E-mail:yangmeih@hust.edu.cn;Jinqiao DUAN,E-mail:duan@iit.edu
  • 基金资助:
    This research was partly supported by NSF (1620449) and NSFC (11531006 and 11771449).

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

Hina ZULFIQAR1, Ziying HE2, Meihua YANG3, Jinqiao DUAN4   

  1. 1. 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;
    2. School of Science, Wuhan University of Technology, Wuhan 430074, China Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China;
    3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    4. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2019-11-18 Revised:2020-04-24 Online:2021-08-25 Published:2021-09-01
  • Supported by:
    This research was partly supported by NSF (1620449) and 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 Laplacian, fast-slow system, stochastic system, random slow manifold, exponential tracking property, parameter estimation

Abstract: 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.

Key words: Nonlocal Laplacian, fast-slow system, stochastic system, random slow manifold, exponential tracking property, parameter estimation

中图分类号: 

  • 35R60