New mathematics to quantify fluctuations and extremes in dynamical systems

量化动力系统波动和极端值的新数学

• 批准号: DP180101223
• 负责人: Prof Gary Froyland
• 金额: $ 28.12万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-01 至 2021-11-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180101223
• 关键词: New; mathematics; quantify; fluctuations; extremes

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.

自然世界中的许多问题是由于复杂动态系统中极端事件的累积效应而产生的。生态和物理过程的动态模型具有内部变量，可以结合起来产生较大的可观察变化。由于明显的确定性组件，动力学及其“长记忆”的时间依赖性，这些混乱模型的可变性的定量估计很困难。该项目旨在开发数学和数字，以准确量化和评估这些复杂的变化。该项目希望提供强大的工具来预测生物地球物理系统中的有害结果，并协助制定缓解策略。