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Strongly asymmetric square waves in a time-delayed system.

Lionel Weicker¹, Thomas Erneux, Otti D'Huys

¹Université Libre de Bruxelles, Optique Nonlinéaire Théorique, Campus Plaine, C.P. 231, 1050 Bruxelles, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 11, 2012

Summary

This summary is machine-generated.

Researchers demonstrate strongly asymmetric square waves in time-delayed systems, with periods near one delay. Plateau lengths are tunable, offering new possibilities for nonlinear dynamics and control.

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Area of Science:

Nonlinear Dynamics
Optoelectronics
Control Theory

Background:

Time-delayed systems typically exhibit symmetric oscillations.
Understanding asymmetric oscillations is crucial for advanced system control.

Purpose of the Study:

To investigate the possibility of strongly asymmetric square waves in time-delayed systems.
To analyze the tunability of plateau lengths and the emergence of these waves.

Main Methods:

Experimental and numerical investigation of a bandpass optoelectronic delay oscillator.
Modeling using nonlinear delay integrodifferential equations.
Asymptotic approximation for large delay analysis.

Main Results:

Demonstrated strongly asymmetric square waves with periods close to one delay.
Showed that plateau lengths are tunable via a control parameter.
Identified asymmetric square waves emerging from a Hopf bifurcation.

Conclusions:

Asymmetric square waves offer novel dynamics in time-delayed systems.
Tunable plateau lengths provide a new control mechanism.
Hopf bifurcation is key to the generation of these asymmetric solutions.