We study globally coupled chaotic maps modeling an optical system, and find clear evidence of nonstatistical behavior: The mean-square deviation (MSD) of the mean field saturates with respect to an increase in the number of elements coupled, after a critical value, and its distribution is clearly non-Gaussian. We also find that the power spectrum of the mean field displays well-defined peaks, indicating a subtle coherence among different elements, even in the "turbulent" phase. This system is a physically realistic model that may be experimentally realizable. It is also a higher-dimensional example (as each individual element is given by a complex map). Its study confirms that the phenomena observed in a wide class of coupled one-dimensional maps are present here as well. This gives more evidence to believe that such nonstatistical behavior is probably generic in globally coupled systems. We also investigate the influence of parametric fluctuations on the MSD.
We study the origin of mixed-mode oscillations and related bifurcations in a fully molecular laser model that describes CO2 monomode lasers with a slow saturable absorber. Our study indicates that the presence of isolas of periodic mixed-mode oscillations, as the pump parameter and the cavity-frequency detuning change, is inherent to Q-switched CO2 monomode lasers. We compare this model, known as the dual four-level model, to the more conventional 3:2 model and to a CO2 laser model for fast saturable absorbers. In these models, we find similarities as well as qualitative differences, such as the different nature of the homoclinic tangency to a relevant unstable periodic orbit, where the Gavrilov-Shilnikov theory and its extensions may hold. We also show that there are isolas of periodic mixed-mode oscillations in a model for CO2 lasers with modulated losses, as the pump parameter varies. The coarse-grained bifurcation diagrams of the periodic mixed-mode oscillations in these models suggest that these oscillations belong to similar classes.
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