New mathematics to quantify fluctuations and extremes in dynamical systems

自然界的许多问题都是复杂动力系统中极端事件的累积效应造成的。生态和物理过程的动态模型具有内部变量，这些变量可以结合起来产生可观察到的大变化。这些混沌模型的可变性的定量估计是困难的，因为动力学的时间依赖性和它们的“长记忆”由于显著的确定性成分。该项目旨在发展数学和数字来准确量化和评估这些复杂的变化。该项目预期将提供强大的工具来预测生物地球物理系统的有害后果，并协助制定缓解战略。

Many problems in the natural world result from the cumulative effect of extreme events in complex dynamical systems. Dynamical models of ecological and physical processes have internal variables that can combine to produce large observable changes. Quantitative estimation of the variability of these chaotic models is difficult because of the time dependence of the dynamics and their “long memory” due to significant deterministic components. This project aims to develop mathematics and numerics to accurately quantify and assess these complicated variations. The project expects to provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.