What predictions can I trust? Stability of chaotic random dynamical systems

该项目旨在对复杂的非自治混沌动力系统的全局稳定性问题取得重大进展。使用遍历理论，该项目期望确定动态模型中的小而频繁的错误或大而不频繁的错误何时以及如何导致有意义的数学模型输出的戏剧性变化。预期的结果包括发现依赖时间的动力系统大范围(IN)稳定性的数学机制，以及检测不稳定性的可靠数值方法。这项研究有望改进对外部驱动动力系统的冲击或崩溃的描述，并帮助科学家衡量他们可以信任的预测。

This project aims to make significant progress on the intricate question of global stability of non-autonomous chaotic dynamical systems. Using ergodic theory, this project expects to determine when and how errors in dynamical models that are small and frequent, or large and infrequent, can cause dramatic changes in meaningful mathematical model outputs. Expected outcomes include the discovery of mathematical mechanisms underlying large-scale (in)stability for time-dependent dynamical systems, and reliable numerical methods for detecting instabilities. This research is expected to lead to improved characterisations of shocks or collapse in externally driven dynamical systems and assist scientists to gauge which predictions they can trust.