Strongly asymmetric square waves in a time-delayed system

Weicker, Lionel, Erneux, Thomas, D'huys, Otti, Danckaert, Jan, Jacquot, Maxime, Chembo, Yanne and Larger, Laurent (2012). Strongly asymmetric square waves in a time-delayed system. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86 (5),


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.

Publication DOI:
Divisions: Engineering & Applied Sciences
Additional Information: ©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
Uncontrolled Keywords: Statistical and Nonlinear Physics,Statistics and Probability,Condensed Matter Physics
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://journal ... sRevE.86.055201 (Publisher URL)
Published Date: 2012-11-29
Authors: Weicker, Lionel
Erneux, Thomas
D'huys, Otti ( 0000-0001-7498-6771)
Danckaert, Jan
Jacquot, Maxime
Chembo, Yanne
Larger, Laurent



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