ABSTRACT
In keeping with the spirit of the Colston conference on Nonlinear Dynamics and Chaos, this chapter emphasizes ideas more than details, describing my vision of how the bifurcation theory of multiple time scale systems will unfold. Multiple time scale dynamical systems arise in modelling diverse phenomena. Examples include equations of chemical reactors, models of boundary layer phenomena in PDE, physical systems such as electrical circuits and lasers, and models within the life sciences. My work has been motivated especially by Hodgkin-Huxleytype models of neural systems [17]. In this setting, the time constants for gating different membrane channels vary by orders of magnitude. Individual neurons, as well as networks, display a rich variety of rhythms. Modelling the generation and modulation of these rhythmic behaviours is a substantial challenge that brings to the fore questions about the bifurcations of multiple time scale systems.
