Nonlinear forecasting of the generalised Kuramoto-Sivashinsky equation

TL;DR

This paper uses nonlinear forecasting to analyze pattern formation and chaos in the generalized Kuramoto-Sivashinsky equation, revealing transitions from chaos to periodic oscillations and demonstrating the method's effectiveness in understanding system dynamics.

Contribution

It introduces a nonlinear forecasting approach to study chaos and pattern formation in the gKS equation, providing new insights into its dynamical transitions.

Findings

Transition from high-dimensional chaos to periodic oscillations

Nonlinear forecasting reveals system's predictability properties

Method applicable to local and global temporal signals

Abstract

We study the emergence of pattern formation and chaotic dynamics 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 with 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.