Bonatto Cristian, Endler Antonio
Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brazil.
Phys Rev E. 2017 Jul;96(1-1):012216. doi: 10.1103/PhysRevE.96.012216. Epub 2017 Jul 18.
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.
我们研究了周期性调制的二氧化碳激光模型中极端和罕见事件的发生情况，即巨脉冲和罕见光脉冲。由于非线性共振过程，我们展示了不同阶次混沌带之间的相互作用情形，这可能导致极端和罕见事件的形成。我们在调制参数空间中确定了一条危机线，并且表明，当调制幅度增加并保持在危机附近时，激光脉冲的一些统计特性，如幅度的平均值和色散，变化不大，而极端事件的幅度则大幅增长，从而产生比通常报道的偏差大得多的极端事件，且具有显著的发生概率，即具有长尾非高斯分布。我们识别出了反复出现的规则模式，即前兆，它们预示着极端和罕见事件的出现，并且我们将这些规则模式与嵌入混沌吸引子中的不稳定周期轨道联系起来。我们表明，前兆可能会也可能不会导致极端事件的出现。因此，一旦在确定性时间序列中识别出前兆，我们就计算预测极端事件成功或失败（误报）的概率。我们表明，这个概率取决于在激光强度时间序列中识别前兆的准确性。
