Multiple-Time-Scale Dynamical Systems

Systems with subprocesses evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neurobiological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple-time-scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori is all explored here. Neurobiology bas played a particularly stimulating role in the development of these techniques, and one paper is directed specifically at applying geometric singular perturbation theory in networks of neural oscillators.