2018/05/12 by Ziying He, He, Ziying, Xinyong Zhang +5
Decision Sciences · Physics and Astronomy · #35R60 #58J65 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Primary: 37L55 #Probabilistic and Robust Engineering Design #Secondary: 60H15 #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1805.04663
openalex publication_date 2018/05/12 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28
We study a Wong-Zakai approximation for the random slow manifold of a slow-fast stochastic dynamical system. We first deduce the existence of the random slow manifold about an approximation system driven by an integrated Ornstein-Uhlenbeck (O-U) process. Then we compute the slow manifold of the approximation system, in order to gain insights of the long time dynamics of the original stochastic system. By restricting this approximation system to its slow manifold, we thus get a reduced slow random system. This reduced slow random system is used to accurately estimate a system parameter of the original system. An example is presented to illustrate this approximation.