Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systems

Tools
- Tools
+ Tools

Parker, M. J., Stewart, Ian and Gomes, M. G. M. (2008) Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systems. International Journal of Bifurcation and Chaos, Vol.18 (No.1). pp. 83-107. doi:10.1142/S0218127408020161

Research output not available from this repository, contact author.
Official URL: http://dx.doi.org/10.1142/S0218127408020161

Request Changes to record.

Abstract

We study perturbations of cubic planforms, proving there exists perturbations with homoclinic cycles between persistent steady states. Our results do not depend on the representation of the symmetry group of the lattice, and are thus quite general. .

The problem is studied using group theory rather than direct methods. We use the abstract action of the symmetry group of the perturbation on the group orbit to determine the existence of zero- and one-dimensional flow-invariant subspaces. The residual symmetry of the perturbation constrains the flows on these subspaces and, in certain cases, homoclinic cycles are guaranteed to exist.

Cubic planforms are physically interesting due to their relevance to certain physical systems. Applications to reaction-diffusion systems, nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction are discussed.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Chaotic behavior in systems, Euclidean algorithm, Bifurcation theory
Journal or Publication Title: International Journal of Bifurcation and Chaos
Publisher: World Scientific Publishing Co. Pte. Ltd.
ISSN: 0218-1274
Official Date: January 2008
Dates:
DateEvent
January 2008Published
Volume: Vol.18
Number: No.1
Number of Pages: 25
Page Range: pp. 83-107
DOI: 10.1142/S0218127408020161
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Funder: Engineering and Physical Sciences Research Council (EPSRC)

Data sourced from Thomson Reuters' Web of Knowledge

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item
twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us