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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2012

Strongly asymmetric square waves in a time-delayed system

Résumé

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.
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Dates et versions

hal-00932485 , version 1 (17-01-2014)

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Lionel Weicker, Thomas Erneux, Otti d'Huys, Jan Danckaert, Maxime Jacquot, et al.. Strongly asymmetric square waves in a time-delayed system. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2012, 86, pp.055201(R). ⟨10.1103/PhysRevE.86.055201⟩. ⟨hal-00932485⟩
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