Strongly asymmetric square waves in a time-delayed system

Lionel Weicker*, Thomas Erneux, Otti D'huys, Jan Danckaert, Maxime Jacquot, Yanne Chembo, Laurent Larger

*Corresponding author for this work

Research output: Contribution to journalArticle

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 number055201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume86
Issue number5
DOIs
Publication statusPublished - 29 Nov 2012

Bibliographical note

©2012 American Physical Society. Strongly asymmetric square waves in a time-delayed system. Lionel Weicker, Thomas Erneux, Otti D’Huys, Jan Danckaert, Maxime Jacquot, Yanne Chembo, and Laurent Larger
Phys. Rev. E 86, 055201(R) – Published 29 November 2012

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    Weicker, L., Erneux, T., D'huys, O., Danckaert, J., Jacquot, M., Chembo, Y., & Larger, L. (2012). Strongly asymmetric square waves in a time-delayed system. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86(5), [055201]. https://doi.org/10.1103/PhysRevE.86.055201