The Oseberg transition: Visualization of global bifurcations for the Kuramoto-Sivashinsky equation

Authors
Johnson, ME Jolly, MS Kevrekidis, IG
Citation
Me. Johnson et al., The Oseberg transition: Visualization of global bifurcations for the Kuramoto-Sivashinsky equation, INT J B CH, 11(1), 2001, pp. 1-18
Citations number
39
Categorie Soggetti
Multidisciplinary
Journal title
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN journal
02181274 → ACNP
Volume
11
Issue
1
Year of publication
2001
Pages
1 - 18
Database
ISI
SICI code
0218-1274(200101)11:1<1:TOTVOG>2.0.ZU;2-S
Abstract
We present and discuss certain global bifurcations involving the interactio n of one- and two-dimensional invariant manifolds of steady and periodic so lutions of the Kuramoto-Sivashinsky equation. Numerical bifurcation calcula tions, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are comb ined in order to characterize what we term the "Oseberg transition".