Martin Wechselberger School of Mathematics and Statistics, University of Sydney Relaxation Oscillatory Patterns - the Geometry of Hodgkin-Huxley Type Models Wednesday 31st May 14:05-14:55pm, Carslaw Building Room 373. Physiological rhythms are central for life. Prominent examples are the beating of the heart, the activity of neurons, or the release of hormones regulating growth and metabolism. The special feature of all these relaxation oscillators is that their dynamics evolve on multiple time scales, long intervals of quasi steady state interspersed by short intervals of rapid variations like the beating of the heart or the firing of action potentials in neurons. These oscillators can create a lot of complicated patterns, many of them not well understood. I will present general results on relaxation oscillatory patterns which are e.g. observed in models of Hodgkin-Huxley (HH) type neurons. Recent work on these HH neurons respectively on neural networks showed a significant slowing of the firing rate under certain circumstances. I show that 'canards' are responsible for that delay and line out how to identify this canard phenomenon in biophysical problems.