My research is broadly in the area of dynamical systems. I study applications of bifurcation theory to 'tipping points' and to spontaneous pattern formation in physical systems. Currently I am especially interested in dynamical systems models related to Earth's climate and ecosystems. My focus is on understanding the mathematical mechanisms behind qualitative changes in system behavior with changes in system parameters. Also of interest are mathematical tipping point mechanisms that involve noise and periodic forcing, or that result from drifting parameters, which may lead to 'rate-induced tipping' in a non-autonomous dynamical systems setting. I want to understand the robustness of these mechanisms to changes in the mathematical model of a problem; this could inform efforts to develop 'early warning signs' of abrupt transitions that may occur as system parameters drift.
