Nonlinear Forecasting of the Generalized Kuramoto-Sivashinsky Equation
File(s)
Accepted version
Author(s)
Gotoda, H
Pradas, M
Kalliadasis, S
Type
Journal Article
Abstract
The emergence of pattern formation and chaotic dynamics is studied in the one-dimensional (1D) generalized Kuramoto–Sivashinsky (gKS) equation by means of a time-series analysis, in particular, a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases that the dynamical state of the gKS solution undergoes a transition from high-dimensional chaos to periodic pulsed oscillations through low-dimensional deterministic chaos while increasing the control parameter of the system. Our results demonstrate that the proposed nonlinear forecasting methodology allows to elucidate the dynamics of the system in terms of its predictability properties.
Date Issued
2015-05-01
Date Acceptance
2014-12-22
Citation
International Journal of Bifurcation and Chaos, 2015, 25 (5)
ISSN
1793-6551
Publisher
World Scientific Publishing
Journal / Book Title
International Journal of Bifurcation and Chaos
Volume
25
Issue
5
Copyright Statement
© 2015 World Scientific Publishing
Subjects
Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Multidisciplinary Sciences
Mathematics
Science & Technology - Other Topics
Spatiotemporal chaos
nonlinear forecasting
pattern formation
SOLITARY PULSES
SPATIOTEMPORAL CHAOS
DISSIPATIVE MEDIA
FALLING FILM
TIME-SERIES
DYNAMICS
SYSTEMS
INSTABILITY
PREDICTION
WAVES
Publication Status
Published
Article Number
ARTN 1530015