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 language | English |
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Article number | 55201 |
Number of pages | 4 |
Journal | Physical Review E |
Volume | 86 |
Issue number | 5 |
Publication status | Published - 29 Nov 2012 |
Keywords
- periodic-solutions
- equations