Self-organization of pulsing and bursting in a CO2 laser with opto-electronic feedback

Abstract

We report a detailed investigation of the stability of a CO2 laser with feedback as described by a six-dimensional rate-equations model which provides satisfactory agreement between numerical and experimental results. We focus on experimentally accessible parameters, like bias voltage, feedback gain, and the bandwidth of the feedback loop. The impact of decay rates and parameters controlling cavity losses are also investigated as well as control planes which imply changes of the laser physical medium. For several parameter combinations, we report stability diagrams detailing how laser spiking and bursting is organized over extended intervals. Laser pulsations are shown to emerge organized in several hitherto unseen regular and irregular phases and to exhibit a much richer and complex range of behaviors than described thus far. A significant observation is that qualitatively similar organization of laser spiking and bursting can be obtained by tuning rather distinct control parameters, suggesting the existence of unexpected symmetries in the laser control space.

Characterizing the dynamics of three FitzHugh-Nagumo neurons network

“…1, and 3) but a general feature was observed in some regions of these diagrams, namely the existence of periodic structures embedded in chaotic regions. These sets of periodic structures are presented in a wide range of nonlinear systems [14]. An exception is in high-dimensional systems with more than three-dimensions, where hyperchaotic behaviors can occur.…”

“…This procedure allows us to identify regions of periodic, chaotic, and hyperchaotic behavior, and recently it is applied in several models. A general feature is observed in these parameter-spaces, the existence of shrimp-shaped periodic structures embedded in chaotic domains [7,14]. These structures are stable periodic domains, i.e., inside them the system variables oscillate periodically with a well-defined period, and often bordered by chaotic regions.…”

“…The colors codify some measure that can be computed on the model. Usually, this measure is the Lyapunov exponent [1,3,7,9,13,14], periods [7,14], or other invariant measure [3]. This procedure allows us to identify regions of periodic, chaotic, and hyperchaotic behavior, and recently it is applied in several models.…”

Stability mosaics in a forced Brusselator

“…As far as we known, the complicated sequences of periodic oscillations unfolding in the low-frequency limit still remain to be investigated. The low-frequency limit is of interest for applications, e.g., to control the onset of pulsations, regular or not, in CO 2 lasers with modulated losses [17][18][19] and in semiconductor lasers [20,21]. This is the oscillatory limit that we address here for the Brusselator, showing that it harbors a plethora of unanticipated and remarkable dynamical phenomena.…”

“…Such computations have been described in detail previously, e.g., in references [17,25] where efficient methods to deal both with numerical and experimental data are given. See also references [19,[26][27][28]. Isospike diagrams require considerably less computations than Lyapunov diagrams.…”