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Slow Manifold and Parameter Estimation for a Nonlocal Fast-Slow Dynamical System with Brownian Motion

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.

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Correspondence to Hina Zulfiqar.

Additional information

This research was partly supported by NSF (1620449) and NSFC (11531006 and 11771449).

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Zulfiqar, H., He, Z., Yang, M. et al. Slow Manifold and Parameter Estimation for a Nonlocal Fast-Slow Dynamical System with Brownian Motion. Acta Math Sci 41, 1057–1080 (2021). https://doi.org/10.1007/s10473-021-0403-y

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Key words

  • Nonlocal Laplacian
  • fast-slow system
  • stochastic system
  • random slow manifold
  • exponential tracking property
  • parameter estimation

2010 MR Subject Classification

  • 35R60