Mixed-mode dynamics

Mixed-mode dynamics is a type of complex oscillatory behaviour that is characterised by an alternation of oscillations of small and large amplitudes. Mixed-mode oscillations (MMOs) frequently occur in fast-slow (’multi-scale’) systems of ordinary differential equations; they are, for instance, found in models from mathematical neuroscience, where they correspond to complicated firing patterns seen in experimental recordings of neural activity. Various mechanisms have been proposed to explain mixed-mode dynamics; however, the relationship between them has not been investigated systematically yet. Moreover, relevant neurological models are typically too high-dimensional to be amenable to mathematical analysis, and have to be reduced efficiently to lower-dimensional normal forms which still capture the essential model dynamics. Informal enquiries can be made to Nikola Popovic ([Email Address Removed]).