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

UNFOLDING THE TORUS - OSCILLATOR GEOMETRY FROM TIME DELAYS

Tools
- Tools
+ Tools

UNSPECIFIED (1993) UNFOLDING THE TORUS - OSCILLATOR GEOMETRY FROM TIME DELAYS. JOURNAL OF NONLINEAR SCIENCE, 3 (4). pp. 459-475.

Research output not available from this repository, contact author.

Request Changes to record.

Abstract

We present a simple method of plotting the trajectories of systems of weakly coupled oscillators. Our algorithm uses the time delays between the ''firings'' of the oscillators. For any system of n weakly coupled oscillators there is an attracting invariant n-dimensional torus, and the attractor is a subset of this invariant torus. The invariant torus intersects a suitable codimension-1 surface of section at an (n - 1)-dimensional torus. The dynamics of n coupled oscillators can thus be reduced, in principle, to the study of Poincare maps of the (n - 1)-dimensional torus. This paper gives a practical algorithm for measuring the n - 1 angles on the torus. Since visualization of 3 (or higher) dimensional data is difficult we concentrate on n = 3 oscillators. For three oscillators, a standard projection of the Poincare map onto the plane yields a projection of the 2-torus which is 4-to-1 over most of the torus, making it difficult to observe the structure of the attractor. Our algorithm allows a direct measurement of the 2 angles on the torus, so we can plot a 1-to-1 map from the invariant torus to the ''unfolded torus'' where opposite edges of a square are identified. In the cases where the attractor is a torus knot, the knot type of the attractor is obvious in our projection.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
Journal or Publication Title: JOURNAL OF NONLINEAR SCIENCE
Publisher: SPRINGER VERLAG
ISSN: 0938-8974
Official Date: 1993
Dates:
DateEvent
1993UNSPECIFIED
Volume: 3
Number: 4
Number of Pages: 17
Page Range: pp. 459-475
Publication Status: Published

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