标题： 赫尔姆霍兹-达芬振荡器中的极端混合模式振荡爆发 显示英文标题

标题： Extreme mixed-mode oscillatory bursts in the Helmholtz-Duffing oscillator

摘要： 我们报告了一种新型的极端事件——极端不规则混合模式振荡爆发——出现在一个不对称的双势阱、受驱动的Helmholtz-Duffing振子中。 系统中三次和二次非线性之间的相互作用，以及外部驱动，导致了这种不寻常的极端事件。 这些极端事件使用阈值以上的方法进行分类，并发现它们与广义极值分布很好地拟合。 其中一个势阱深度的不对称性使得振子能够在两个势阱之间表现出罕见的不规则混合模式振荡，表现为极度不规则的混合模式振荡爆发。 此外，我们还发现，这种在两个势阱之间的不规则转换发生在周期性外部驱动的上升阶段。 重要的是，我们还发现系统的速度可以被跟踪并用作这种新型极端事件发生的可靠领先指标。 显示英文摘要

摘要： We report a new type of extreme event - extreme irregular mixed-mode oscillatory burst - appearing in an asymmetric double-welled, driven Helmholtz-Duffing oscillator. The interplay of cubic and quadratic nonlinearities in the system, along with the external drive, contributes to this type of unusual extreme event. These extreme events are classified using the peak-over threshold method and found to be well-fitted with the generalized extreme value distribution. The asymmetry in the depth of one of the potential wells allows the oscillator to exhibit rare irregular mixed-mode oscillations between the two wells, manifesting as extremely irregular mixed-mode oscillatory bursts. Furthermore, we also find that such an irregular transition between the two potential wells occurs during the up phase of the periodic external drive. Importantly, we also find that the system velocity can be tracked and utilized as a reliable lead indicator of the occurrence of this novel type of extreme event.