Classification of chaos and quasiperiodicity using artificial neural network

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, support vector machines and artificial neural networks. 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 obtain accuracy of binary classification up to 87% with artificial neural network.

Speaker

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

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