New mathematics to unravel dynamical systems in changing environments (2025-2029)
Abstract
Randomness and predictability are ubiquitous in daily life. This project aims to resolve crucial gaps in understanding how environment changes affect the transient and long-term behaviour of chaotic systems influenced by noisy inputs and external forces. Using modern ergodic theory, this project expects to generate novel mathematical tools to analyse complex dynamical systems, including models of natural and human systems, and refined limit laws explaining fluctuations in random dynamical systems. Project benefits include the development of breakthrough mathematics with potentially broad impact in science and technology, high-quality training of Australian scientists and enhanced international collaboration in the mathematical sciences.
