Frequency and peak discontinuities in self-pulsations of a CO2 laser with feedback

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

“…From the point of view of simulations, the stability diagrams for the six dimensional model corroborate previous findings obtained for the simpler three dimensional model, 49 but go well beyond them. Considering the relevance of the CO 2 laser with optoelectronic feedback in nonlinear dynamics, a detailed investigation taking advantage from the novel isospike technique [39][40][41][42][43][44][45][46] has been proposed.…”

“…However, the isospike diagram informs simultaneously how the complexification of the laser signal occurs, i.e., it shows how to tune parameters in order to obtain more and more spikes in the laser oscillation via continuous deformations that create and destroy peaks, as described recently for the infinite-dimensional Mackey-Glass delayed feedback system 48 and for a CO 2 laser with feedback model governed by three differential equations. 49 From now on, we will describe laser stability using the more detailed diagrams obtained by classifying systematically the number of spikes of the laser oscillations.…”

Stability mosaics in a forced Brusselator

“…Of interest was to understand the partitioning of large portions of the control parameter space into cascades of stability phases and their intricate accumulations. The stability diagrams reported here differ considerably from the ones familiar for, e.g., lasers [20,21,31], chemical [27,32], biochemical oscillators [33], and even for a novel psychological stress variation model [34]. A startling observation reported here is an apparently infinite sequence of signals that are not self-antiperiodic as usual but, instead, are antiperiodic to another oscillation in the group.…”

“…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.…”

Nonlinear Models for the Delayed Immune Response to a Viral Infection

“…To cite a few, in [6], the authors describe continuous deformations in periodic solutions of the onedimensional Mackey-Glass equation, a standard model for delayed feedback systems [7]. In [8], it is analyzed selfpulsations in laser beams with feedback. Reference [9] considers sigmoid maps, which display a locking behavior observed in several systems, and its relation with the Stern-Brocot tree, a binary tree whose vertices correspond to the positive rational numbers [10,11].…”