dc.contributor.author |
Postlethwaite, Claire |
en |
dc.date.accessioned |
2012-03-13T01:05:41Z |
en |
dc.date.issued |
2009 |
en |
dc.identifier.citation |
SIAM Journal on Applied Dynamical Systems 8(1):21-39 2009 |
en |
dc.identifier.issn |
1536-0040 |
en |
dc.identifier.uri |
http://hdl.handle.net/2292/14128 |
en |
dc.description.abstract |
The Pyragas method of feedback control has attracted much interest as a method of stabilizing unstable periodic orbits in a number of situations. We show that a time-delayed feedback control similar to the Pyragas method can be used to stabilize periodic orbits with arbitrarily large period, specifically those resulting from a resonant bifurcation of a heteroclinic cycle. Our analysis reduces the infinite-dimensional delay-equation governing the system with feedback to a three-dimensional map, by making certain assumptions about the form of the solutions. The stability of a fixed point in this map corresponds to the stability of the periodic orbit in the flow and can be computed analytically. We compare the analytic results to a numerical example and find very good agreement. |
en |
dc.publisher |
Society for Industrial and Applied Mathematics |
en |
dc.relation.ispartofseries |
SIAM Journal on Applied Dynamical Systems |
en |
dc.rights |
Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.sherpa.ac.uk/romeo/issn/1536-0040/ |
en |
dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
en |
dc.title |
Stabilization of long-period periodic orbits using time-delayed feedback control |
en |
dc.type |
Journal Article |
en |
dc.identifier.doi |
10.1137/080721510 |
en |
pubs.issue |
1 |
en |
pubs.begin-page |
21 |
en |
pubs.volume |
8 |
en |
dc.rights.holder |
Copyright: Society for Industrial and Applied Mathematics |
en |
pubs.end-page |
39 |
en |
dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
en |
pubs.subtype |
Article |
en |
pubs.elements-id |
88008 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
Mathematics |
en |
pubs.arxiv-id |
0804.2903 |
en |
pubs.record-created-at-source-date |
2010-09-01 |
en |