Speaker
Description
A challenge in modelling biological phenomena is that the resulting models often involve many interacting variables that exhibit complex nonlinear dynamics, making them difficult to study using dynamical systems theory. The well-established theory behind the Koopman operator helps to address this challenge by representing complex nonlinear models as simpler, linear models evolving in an infinite-dimensional function space, where one can take advantage of the linearity to study the model in a new context. Many numerical methods have been developed that are able to uncover finite-dimensional approximations of the Koopman operator using observed or simulated data from dynamical systems. The eigenfunctions of the (approximated) Koopman operator can then be used to estimate information about the original system, including stable equilibria and their respective basins of attraction. In this presentation, we explore the utility of Koopman operator theory in a mathematical biology setting by applying these methods to recover the dynamics of well-studied chemostat models. We also present preliminary results in applying these methods to recover the dynamics of a more complex model of a gut bioreactor.
