Theodore Vo: Canards, Cardiac Cycles, and Chimeras

Abstract: Canards are solutions of singularly perturbed ODEs that organise the dynamics in phase and parameter space. In this talk, we explore two aspects of canard theory: their applications in the life sciences and their ability to generate new phenomena. More specifically, we will use canard theory to analyse a canonical model of the electrical activity in a heart muscle cell. We demonstrate that pathological heart rhythms, called early afterdepolarisations, are canard-induced phenomena. We use this knowledge to explain the rich set of model behaviours, some of which have also been observed in experiments. Then, we explore a new class of canard-induced patterns in reaction-diffusion PDEs which exhibit coexisting domains of mutually synchronised oscillators and complementary domains of decoherent (asynchronous) oscillators.