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

M. E. Johnson; M. S. Jolly; I. G. Kevrekidis

doi:10.1142/S0218127401001979

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

M. E. Johnson
, M. S. Jolly
, I. G. Kevrekidis

Chemical & Biological Engineering

Research output: Contribution to journal › Review article › peer-review

21 Scopus citations

Abstract

We present and discuss certain global bifurcations involving the interaction of one- and two- dimensional invariant manifolds of steady and periodic solutions of the Kuramoto-Sivashinsky equation. Numerical bifurcation calculations, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are combined in order to characterize what we term the "Oseberg transition".

Original language	English (US)
Pages (from-to)	1-18
Number of pages	18
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	11
Issue number	1
DOIs	https://doi.org/10.1142/S0218127401001979
State	Published - Jan 2001

All Science Journal Classification (ASJC) codes

Modeling and Simulation
Engineering (miscellaneous)
General
Applied Mathematics

Access to Document

10.1142/S0218127401001979

Cite this

@article{0c32888c36d64884b5bd34a081ccb590,

title = "The Oseberg transition: Visualization of global bifurcations for the Kuramoto-Sivashinsky equation",

abstract = "We present and discuss certain global bifurcations involving the interaction of one- and two- dimensional invariant manifolds of steady and periodic solutions of the Kuramoto-Sivashinsky equation. Numerical bifurcation calculations, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are combined in order to characterize what we term the {"}Oseberg transition{"}.",

author = "Johnson, \{M. E.\} and Jolly, \{M. S.\} and Kevrekidis, \{I. G.\}",

note = "Funding Information: We thank the National Science Foundation for continuing support over the years we have been exploring the dynamics of the KSE. During that period, good portions of that effort came while all three authors enjoyed the hospitality of both the Center for Nonlinear Studies at the Los Alamos National Laboratory and the Institute of Mathematics and its Applications at the University of Minnesota. This work constitutes a part of the PhD thesis of M. E. Johnson in the Program in Applied and Computational Mathematics at Princeton University. This paper is dedicated to the Torrey Pines Foundation which, for many years and in many ways, has supported the research of I. G. Kevrekidis and M. S. Jolly.",

year = "2001",

month = jan,

doi = "10.1142/S0218127401001979",

language = "English (US)",

volume = "11",

pages = "1--18",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "World Scientific",

number = "1",

}

TY - JOUR

T1 - The Oseberg transition

T2 - Visualization of global bifurcations for the Kuramoto-Sivashinsky equation

AU - Johnson, M. E.

AU - Jolly, M. S.

AU - Kevrekidis, I. G.

N1 - Funding Information: We thank the National Science Foundation for continuing support over the years we have been exploring the dynamics of the KSE. During that period, good portions of that effort came while all three authors enjoyed the hospitality of both the Center for Nonlinear Studies at the Los Alamos National Laboratory and the Institute of Mathematics and its Applications at the University of Minnesota. This work constitutes a part of the PhD thesis of M. E. Johnson in the Program in Applied and Computational Mathematics at Princeton University. This paper is dedicated to the Torrey Pines Foundation which, for many years and in many ways, has supported the research of I. G. Kevrekidis and M. S. Jolly.

PY - 2001/1

Y1 - 2001/1

N2 - We present and discuss certain global bifurcations involving the interaction of one- and two- dimensional invariant manifolds of steady and periodic solutions of the Kuramoto-Sivashinsky equation. Numerical bifurcation calculations, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are combined in order to characterize what we term the "Oseberg transition".

AB - We present and discuss certain global bifurcations involving the interaction of one- and two- dimensional invariant manifolds of steady and periodic solutions of the Kuramoto-Sivashinsky equation. Numerical bifurcation calculations, dimensionality reduction using approximate inertial manifolds/forms, as well as approximation and visualization of invariant manifolds are combined in order to characterize what we term the "Oseberg transition".

UR - https://www.scopus.com/pages/publications/0034747501

UR - https://www.scopus.com/pages/publications/0034747501#tab=citedBy

U2 - 10.1142/S0218127401001979

DO - 10.1142/S0218127401001979

M3 - Review article

AN - SCOPUS:0034747501

SN - 0218-1274

VL - 11

SP - 1

EP - 18

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this