Recent work on multiple-timescale dynamical systems has overwhelmingly focused on models where there is a global identification of “slow” versus “fast” variables throughout the phase space. But in many physical models, this standard assumption can be unnecessarily restrictive: for example, many chemical reaction networks have distinguished slow versus fast reactions, but each individual chemical concentration may change slowly or rapidly along a typical trajectory.
This talk discusses two recent developments in nonstandard slow-fast systems. The first is the use of the computational singular perturbation (CSP) method to approximate invariant slow manifolds and fast fibers. The second is the classification of contact singularities and bifurcations in terms of a natural algebraic factorisation of the vector field. We apply these algorithms and techniques to a variety of applied problems.
Ian Lizarraga is a postdoctoral fellow working in the School of Mathematics and Statistics at the University of Sydney. He received his PhD in Applied Mathematics at Cornell University, where he studied bifurcation problems in slow-fast dynamical systems with John Guckenheimer and model reduction in coupled oscillators with Steven Strogatz.