Strongly asymmetric square waves in a time-delayed system

L. Weicker, Thomas Erneux, Ottilde D'Huys, Jan Danckaert, M. Jacquot, Y. Chembo, L. Larger

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)

Abstract

Time-delayed systems are known to exhibit symmetric square waves oscillating with a period close to twice the delay. Here, we show that strongly asymmetric square waves of a period close to one delay are possible. The plateau lengths can be tuned by changing a control parameter. The problem is investigated experimentally and numerically using a simple bandpass optoelectronic delay oscillator modeled by nonlinear delay integrodifferential equations. An asymptotic approximation of the square-wave periodic solution valid in the large delay limit allows an analytical description of its main properties (extrema and square pulse durations). A detailed numerical study of the bifurcation diagram indicates that the asymmetric square waves emerge from a Hopf bifurcation.
Original languageEnglish
Article number55201
Number of pages4
JournalPhysical Review E
Volume86
Issue number5
Publication statusPublished - 29 Nov 2012

Keywords

  • periodic-solutions
  • equations

Fingerprint

Dive into the research topics of 'Strongly asymmetric square waves in a time-delayed system'. Together they form a unique fingerprint.

Cite this