Related papers: Practical implementation of nonlinear time series …

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

In this paper, we present a nonlinear analysis software toolkit, which can help in biomechanical gait data analysis by implementing various nonlinear statistical analysis algorithms. The toolkit is proposed to tackle the need for an…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

We introduce PyChEst, a Python package which provides tools for the simultaneous estimation of multiple changepoints in the distribution of piece-wise stationary time series. The nonparametric algorithms implemented are provably consistent…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…

Benchmarking anomaly detection approaches for multivariate time series is a challenging task due to a lack of high-quality datasets. Current publicly available datasets are too small, not diverse and feature trivial anomalies, which hinders…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…

We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

Scientific fields such as insider-threat detection and highway-safety planning often lack sufficient amounts of time-series data to estimate statistical models for the purpose of scientific discovery. Moreover, the available limited data…

Time series data is used in a wide range of real world applications. In a variety of domains , detailed analysis of time series data (via Forecasting and Anomaly Detection) leads to a better understanding of how events associated with a…

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…

Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…

This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…