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.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 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