Cristian Bonatto

Self-Similarities in the Frequency-Amplitude Space of a Loss-Modulated CO2 Laser

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings could be isomorphic.

Accumulation horizons and period adding in optically injected semiconductor lasers

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable accumulation horizons: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as, e.g., secure communications.

Accumulation boundaries: codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric and chemical oscillators.

We report high-resolution phase diagrams for several familiar dynamical systems described by sets of ordinary differential equations: semiconductor lasers; electric circuits; Lorenz-84 low-order atmospheric circulation model; and Rössler and chemical oscillators. All these systems contain chaotic phases with highly complicated and interesting accumulation boundaries, curves where networks of stable islands of regular oscillations with ever-increasing periodicities accumulate systematically. The experimental exploration of such codimension-two boundaries characterized by the presence of infinite accumulation of accumulations is feasible with existing technology for some of these systems.

Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model

We report phase diagrams detailing the intransitivity observed in the climate scenarios supported by a prototype atmospheric general circulation model, namely, the Lorenz-84 low-order model. So far, this model was known to have a pair of coexisting climates described originally by Lorenz. Bifurcation analysis allows the identification of a remarkably wide parameter region where up to four climates coexist simultaneously. In this region the dynamical behavior depends crucially on subtle and minute tuning of the model parameters. This strong parameter sensitivity makes the Lorenz-84 model a promising candidate of testing ground to validate techniques of assessing the sensitivity of low-order models to perturbations of parameters.

Extreme and superextreme events in a loss-modulated CO2 laser : nonlinear resonance route and precursors

We investigate the occurrence of extreme and rare events, i.e., giant and rare light pulses, in a periodically modulated CO_{2} laser model. Due to nonlinear resonant processes, we show a scenario of interaction between chaotic bands of different orders, which may lead to the formation of extreme and rare events. We identify a crisis line in the modulation parameter space, and we show that, when the modulation amplitude increases, remaining in the vicinity of the crisis, some statistical properties of the laser pulses, such as the average and dispersion of amplitudes, do not change much, whereas the amplitude of extreme events grows enormously, giving rise to extreme events with much larger deviations than usually reported, with a significant probability of occurrence, i.e., with a long-tailed non-Gaussian distribution. We identify recurrent regular patterns, i.e., precursors, that anticipate the emergence of extreme and rare events, and we associate these regular patterns with unstable periodic orbits embedded in a chaotic attractor. We show that the precursors may or may not lead to the emergence of extreme events. Thus, we compute the probability of success or failure (false alarm) in the prediction of the extreme events, once a precursor is identified in the deterministic time series. We show that this probability depends on the accuracy with which the precursor is identified in the laser intensity time series.

On the interaction of focused electromagnetic beams and space-charge fields in laser-plasma systems

In the present analysis we study the weakly nonlinear coupled dynamics involving focused radiation beams and spacecharge fields in laser-plasmas systems. We direct the analysis to regimes evolving with the co-moving coordinate of the beam frame, but do not make any assumptions on paraxial or underdense conditions. The model thus constructed allows us to investigate equilibrium and nonequilibrium regimes alike. Dependence of equilibrium profiles on control parameters is examined, and beam stability and evolution is investigated as one adds small mismatches to the ideally matched equilibrium. Details of beam evolution depend on initial conditions. However, independently of the precise form of initial conditions, mismatched beams evolve to incoherent space-time patterns.