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

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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
Issue number5
Publication statusPublished - 1 Nov 2012
Externally publishedYes


  • Nonlinear dynamics and chaos
  • Dynamics of nonlinear optical systems
  • optical instabilities optical chaos and complexity and optical spatio-temporal dynamics
  • Delay and functional equations
  • Bifurcation theory

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