Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms
Fecha
2022-08-27Tipo de documento
articleÁrea/s de conocimiento
Matemáticas y FísicaMateria/s Unesco
12 MatemáticasResumen
Most of the existing methods and techniques for the detection of chaotic behaviour
from empirical time series try to quantify the well-known sensitivity to initial conditions
through the estimation of the so-called Lyapunov exponents corresponding to the data
generating system, even if this system is unknown. Some of these methods are designed
to operate in noise-free environments, such as those methods that directly quantify the
separation rate of two initially close trajectories. As an alternative, this paper provides
two nonlinear indirect regression methods for estimating the Lyapunov exponents on a
noisy environment. We extend the global Jacobian method, by using local polynomial kernel regressions and local neural net kernel models. We apply such methods to several
noise-contaminated time series coming from different data generating processes. The results show that in general, the Jacobian indirect methods provide better results than the
traditional direct methods for both clean and noisy time series. Moreover, the local Jacobian indirect methods provide more robust and accurate fit than the global ones, with
the methods using local networks obtaining more accurate results than those using local
polynomials.