Tools for time series analysis of nonlinear dynamical systems

Abstract

Nonlinear dynamical systems analysis is a very important part of numerous areas of research. Study of deterministic chaos is a key tool to determine the dynamics of systems, which are hard to explain by classical methods. However, estimating dynamical properties of a system using the experimental data is a difficult task. Specifically, a computational complexity of many tools for the nonlinear analysis of dynamical system makes it impossible to estimate the results for the large datasets. This work focuses on parallelization and application of the computationaly expensive methods such as recurrence quantitative analysis and the 0-1 test for chaos. Comparison of these methods with the classical methods is made and the strengths and weaknesses of each method are discussed.