Hinke Osinga

The art of computing global manifolds

Global manifolds are the backbone of a dynamical system and key to the characterisation of its behaviour. They arise in the classical sense of invariant manifolds associated with saddle-type equilibria or periodic orbits and, more recently, in the form of finite-time invariant manifolds in system that evolve on multiple time scales. Dynamical systems theory relies heavily on the knowledge of such manifolds, because of the geometric insight that they can offer into how observed behaviour arises. In applications, global manifolds need to be computed and visualised so that quantitative information about the overall system dynamics can be obtained. This requires accurate numerical methods and a precise understanding of how the computations depend on various model parameters. The computation of global manifolds is a serious challenge, but an effort that pays off. This talk will focus on two case studies that represent the most recent developments in this area.