# Daniel Gauthier : Nonlinear stability analysis of a time-delay opto-electronic oscillator

I will describe some recent work on the dynamics of an optoelectronic time-delay oscillator that displays high-speed chaotic behavior with a flat, broad power spectrum. The chaotic state coexists with a linearly stable fixed point, which, when subjected to a finite-amplitude perturbation, loses stability initially via a periodic train of ultrafast pulses. A nonlinear stability analysis is required to understand the device dynamics. Through such an analysis, an approximate mapping is derived that does an excellent job of capturing the observed instability. The oscillator provides a simple device for fundamental studies of time-delay dynamical systems and can be used as a building block for ultrawide-band sensor networks. The results of this study recently appeared in print and can be found here: PRL The work is the part of Kristine Callan's PhD dissertation research and was in collaboration with Zheng Gao, Lucas Illing, and Eckehard Schoell.

**Category**: Nonlinear and Complex Systems**Duration**: 01:39:43**Date**: April 27, 2010 at 2:45 PM-
**Tags:**seminar, CNCS Seminar

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