Applied Maths Seminar: Weckesser -- Reduced System Computing for Singularly Perturbed Differential Equations

A singularly perturbed system of differential equations can be reduced, in the singular
limit, to a system in which the dynamics are given by the concatenation of two lower
dimensional systems, called the fast and slow subsystems.  Local and global bifurcations
of the reduced system can imply similar bifurcations of the original system.
Canards--solutions that remain close to unstable slow manifolds for a long time--play a
key role in this analysis.  I will present analyses and numerical studies of some of the
bifurcations of periodic orbits of reduced systems.  Examples will include the forced
van der Pol system and models of coupled neurons.