Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (4): 1057-1080.doi: 10.1007/s10473-021-0403-y

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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).

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

CLC Number: 

  • 35R60
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