In order to capture a more realistic portrait of the dynamics of a given population, some modern mathematical models account for individual variability by introducing continuous variables to which we refer as “structures”. They represent physical or physiological traits that influence individual vital rates (such as birth or mortality). Examples are age, size, sex and immunity level.
Structured populations can be formulated as first-order hyperbolic partial differential equations, depending on time and other spatial variables that represent the structures. These models tipically generate dynamical systems acting on abstract spaces (of functions).
From the dynamical systems point of view, one is interested in studying the linearized dynamics in view of assessing the local stability of, e.g., equilibria or other invariants. This tipically leads to investigate the spectrum of linear operators acting between infinite-dimensional vector spaces and, most of times, it can not be achivied analitically.
My research thus deals with the study of numerical methods for approximating the spectrum of those operators governing the linearized dynamics, both from the computational and the theoretical standpoint.