动力系统中极端事件的路径：动力学和统计特征
Routes to extreme events in dynamical systems: Dynamical and Statistical Characteristics
摘要：
在许多动力系统的状态变量的时间演化过程中，可以看到间歇性的大振幅事件。这种间歇性的大事件突然开始出现在动力系统中的一个系统参数的临界值，并继续为一系列的参数值。三个重要的不稳定性过程，即内部危机，Pomeau-Manneville不稳定性和准周期运动的崩溃，是最常见的，在许多系统中观察到，导致这种偶尔和罕见的过渡到大振幅尖峰事件。我们将这些偶尔发生的大事件描述为极端事件，如果它们大于统计定义的显著高度。我们提出了两个示例性的系统，一个单一的系统和耦合系统来说明如何工作的不稳定性起源于极端事件，他们表现为非平凡的动力学事件。我们说明了这样的事件的动力学和统计特性。
英文摘要：
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and continues for a range of parameter values. Three important processes of instabilities, namely, interior crisis, Pomeau-Manneville intermittency and the breakdown of quasiperiodic motion, are most common as observed in many systems that lead to such occasional and rare transitions to large amplitude spiking events. We characterize these occasional large events as extreme events if they are larger than a statistically defined significant height. We present two exemplary systems, a single system and a coupled system to illustrate how the instabilities work to originate as extreme events and they manifest as non-trivial dynamical events. We illustrate the dynamical and statistical properties of such events.
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