Back and forth between the infinite and the finite: a numerical view of time delay systems
The view of delay differential equations as generators of dynamical systems evolving on function spaces has fostered substantial and essential progress in the study and understanding of these equations since the inspiring works of Krasovskii in the fifties. Of course the price to pay to exploit this enlarged perspective is that of dealing with infinite dimension. On the one hand, the functional analysis of Banach spaces has helped to extend to delay systems well known results holding for ODEs — often with (un)expected difficulties. On the other hand, discretization tools of numerical analysis have entered the scene as a natural way to bring infinite-dimensional objects back to finite ones in view of attaining — hopefully trustworthy approximate — solutions to the considered problems. The talk is about some of the aspects concerned with the interplay between these finite- and infinite-dimensional contexts, mainly in view of numerically addressing questions of stability and bifurcation.
The seminar is part of the IFAC TDS webinar series.
