New mathematics to quantify fluctuations and extremes in dynamical systems (ARC Discovery Project administered by the University of New South Wales) (2018-2021)

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 will develop cutting-edge mathematics and numerics to accurately quantify and assess these complicated variations. Our breakthrough mathematics will provide powerful tools to predict harmful outcomes in biogeophysical systems, and assist with the development of mitigation strategies.