RT Journal Article
T1 Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms
A1 Escot Mangas, Lorenzo
A1 Sandubete Galán, Julio Emilio
A2 Simos, Theodore E.
AB 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.
PB Elsevier
SN 0096-3003
YR 2023
FD 2023-01-01
LK https://hdl.handle.net/20.500.14352/99625
UL https://hdl.handle.net/20.500.14352/99625
LA eng
NO Escot, L.; Sandubete, J.E., “Estimating Lyapunov exponents on a noisy environment by global and local Jacobian indirect algorithms”. J. Applied Mathematics and Computation, (0096-3003), vol 436, 1 January, 2023, 127498.
NO Goverment of Spain
NO Faculty of Statistical Studies
NO Computing and Artificial Itelligence Lab - Camilo José Cela University
NO Data Analysis in Social and Gender Studies and Equality Policies UCM Research Group (www.ucm.es/aedipi/)
DS Docta Complutense
RD 21 jul 2024