Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behavior in the case of two delays is shown to "encode" two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the long-delay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.
Pattern Formation in Systems with Multiple Delayed Feedbacks
Giovanni Giacomelli
2014
Abstract
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behavior in the case of two delays is shown to "encode" two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the attainment of the long-delay regime is introduced. We also demonstrate this phenomenon for a semiconductor laser with two delayed optical feedbacks.File | Dimensione | Formato | |
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