Year: 2009
Type: article
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.
DOI: 10.1137/080721510
Author: Claire M. Postlethwaite
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2013987972