Related papers: A parameter estimation method based on random slow…

This work is about parameter estimation for a fast-slow stochastic system with non-Gaussian $\alpha$-stable L\'evy noise. When the observations are only available for slow components, a system parameter is estimated and the accuracy for…

We establish a slow manifold for a fast-slow stochastic evolutionary system with anomalous diffusion, where both fast and slow components are influ- enced by white noise. Furthermore, we prove the exponential tracking property for the…

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…

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…

Multiple time scale stochastic dynamical systems are ubiquitous in science and engineering, and the reduction of such systems and their models to only their slow components is often essential for scientific computation and further analysis.…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

We consider the relation for the stochastic equilibrium states between the reduced system on a random slow manifold and the original system. This provides a theoretical basis for the reduction about sophisti- cated detailed models by the…

We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…

We propose a simple method to estimate the parameters involved in discrete dynamical systems from time series. The method is based on the concept of controlling chaos by constant feedback. The major advantages of the method are that it…

This work is about a slow-fast data assimilation system when only slow components are observable. First, we obtain its low dimensional reduction via an invariant slow manifold. Second, we prove that the low dimensional filter on the slow…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…

We propose a robust parameter estimation method for dynamical systems based on Statistical Learning techniques which aims to estimate a set of parameters that well fit the dynamics in order to obtain robust evidences about the qualitative…

We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…

The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is…

A stochastic mode reduction strategy is applied to multiscale models with a deterministic energy-conserving fast sub-system. Specifically, we consider situations where the slow variables are driven stochastically and interact with the fast…