Abstract
This paper discusses the neural network approach for computing of Lyapunov spectrum using one dimensional time series from unknown dynamical system. Such an approach is based on the reconstruction of attractor dynamics and applying of multilayer perceptron (MLP) for forecasting the next state of dynamical system from the previous one. It allows for evaluating the Lyapunov spectrum of unknown dynamical system accurately and efficiently only by using one observation. The results of experiments are discussed.
Highlights
Processing of time series often turns out to be insufficient when the data irregular and this inadequacy has often been assigned to noise and randomness
In practice, the existing approaches for the estimation of the Lyapunov exponents from experimental data are characterized by computational complexity, require a large data length and applied only when we have all observations of dynamical system
After training neural network and starting from a given initial condition, this network is able to compute the state of the dynamical system at any time, as well as to describe the evolution of the phase trajectory points
Summary
Processing of time series often turns out to be insufficient when the data irregular and this inadequacy has often been assigned to noise and randomness. Many real dynamical systems (e.g., compound pendula, dripping faucets, chemical reactions, stock market, EEG patterns of brainwave activity, social behaviour) are believed to be nonlinear. In many such systems, chaotic behaviour has been observed. In practice, the existing approaches for the estimation of the Lyapunov exponents from experimental data are characterized by computational complexity, require a large data length and applied only when we have all observations of dynamical system. In this paper is proposed new approach for computing of Lyapunov spectrum using only one-dimensional observations from unknown dynamical system.
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