Generative learning for nonlinear dynamics

W Gilpin - Nature Reviews Physics, 2024‏ - nature.com
Modern generative machine learning models are able to create realistic outputs far beyond
their training data, such as photorealistic artwork, accurate protein structures or …

Data based identification and prediction of nonlinear and complex dynamical systems

WX Wang, YC Lai, C Grebogi - Physics Reports, 2016‏ - Elsevier
The problem of reconstructing nonlinear and complex dynamical systems from measured
data or time series is central to many scientific disciplines including physical, biological …

Chaos as an intermittently forced linear system

SL Brunton, BW Brunton, JL Proctor, E Kaiser… - Nature …, 2017‏ - nature.com
Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

Horizontal visibility graphs: Exact results for random time series

B Luque, L Lacasa, F Ballesteros, J Luque - Physical Review E—Statistical …, 2009‏ - APS
The visibility algorithm has been recently introduced as a map** between time series and
complex networks. This procedure allows us to apply methods of complex network theory for …

Nonlinear dynamical analysis of EEG and MEG: review of an emerging field

CJ Stam - Clinical neurophysiology, 2005‏ - Elsevier
Many complex and interesting phenomena in nature are due to nonlinear phenomena. The
theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a …

[کتاب][B] Time-series analysis and cyclostratigraphy: examining stratigraphic records of environmental cycles

GP Weedon - 2003‏ - books.google.com
Increasingly, environmental scientists, palaeoceanographers and geologists are collecting
quantitative records of environmental changes (time series) from sediments, ice cores, cave …

Nonlinear forecasting for the classification of natural time series

G Sugihara - … Transactions of the Royal Society of …, 1994‏ - royalsocietypublishing.org
There is a growing trend in the natural sciences to view time series as products of dynamical
systems. This viewpoint has proven to be particularly useful in stimulating debate and insight …

Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series

M Zanin, F Olivares - Communications Physics, 2021‏ - nature.com
One of the most important aspects of time series is their degree of stochasticity vs. chaoticity.
Since the discovery of chaotic maps, many algorithms have been proposed to discriminate …

Description of stochastic and chaotic series using visibility graphs

L Lacasa, R Toral - Physical Review E—Statistical, Nonlinear, and Soft …, 2010‏ - APS
Nonlinear time series analysis is an active field of research that studies the structure of
complex signals in order to derive information of the process that generated those series, for …

Emergence of a resonance in machine learning

ZM Zhai, LW Kong, YC Lai - Physical Review Research, 2023‏ - APS
The benefits of noise to applications of nonlinear dynamical systems through mechanisms
such as stochastic and coherence resonances have been well documented. Recent years …