标题： 希格斯振荡器中的极端事件：动力学研究与预测方法 显示英文标题

标题： Extreme Events in the Higgs Oscillator: A Dynamical Study and Forecasting Approach

摘要： 许多动力系统在状态变量的时间进程中表现出意外的大振幅偏移。 在本研究中，我们考虑与一维希格斯振子相关的动力学，该振子通过将定义在具有恒定曲率的球面空间上的谐振子进行gnomic投影，映射到与球面空间相切的欧几里得平面上实现。 在研究这种受到阻尼和外部激励的希格斯振子的动力学时，遇到了各种分岔现象，如对称性破缺、周期倍增和间歇性危机。 随着驱动参数的增加，混沌的路径是通过间歇性危机发生的，我们还确认了由于内部危机导致极端事件的发生。 概率分布的研究也证实了极端事件的发生。 最后，我们使用时间序列数据训练长短期记忆神经网络模型来预测极端事件（EEs）。 显示英文摘要

摘要： Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator which is realized through gnomic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the Long Short-Term Memory neural network model with the time-series data to forecast the extreme events (EEs).