Classification of chaos and quasiperiodicity using machine learning

Abstract

In presented work we suggest a novel method of classification of chaotic and quasiperiodic oscillations by its time series. It is known that a number of characteristics usually is needed to determine chaotical dynamic such as Lyapunov exponents, correlation and covariance analysis, Fourier spectrum etc. Calculating Lyapunov exponents based only on a time series is a separate and difficult task. Calculation of other characteristics in the case of significant signal durations (this is an important condition for establishing their stationarity!) can take a lot of time.
We propose an alternative approach in which a set of simple statistical characteristics of the signal (mean, variance, kurtosis etc.) is calculated, which is then used to operate various classifiers, such as k nearest neighbors, k means and others. As a result, it is expected to obtain a classifier that allows to determine from the statistical characteristics whether the oscillations are chaotic or quasi-periodic for an arbitrary time series.
In presented work we compare accuracy of classification for different dynamical systems and different machine learning methods.

Speaker

A. D. Ryabchenko
Saratov State University, Saratov, Russia.
Russia

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