New mathematics to quantify fluctuations and extremes in dynamical systems

自然界中的许多问题都是复杂动力系统中极端事件累积效应的结果。生态和物理过程的动力学模型有内部变量，可以结合在一起产生巨大的可观察到的变化。这些混沌模型的变异性的定量估计是困难的，因为动力学具有时间依赖性，并且由于具有显著的确定性成分而具有“长记忆性”。这个项目的目的是发展数学和数值来准确地量化和评估这些复杂的变化。该项目预计将提供强大的工具来预测生物地球物理系统中的有害结果，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.