Multiple time scale dynamics and geometry of a model for bipolar disorders

In this talk an ODE system modeling oscillatory patterns of mood alternations in manic-depression, also known as bipolar disorder, is analyzed. The model is four-dimensional, contains many parameters of different orders of magnitude, and non-polynomial nonlinearities. This poses several challenges and the analysis of the model must be based on identifying and using hierarchies of local approximations based on various –- hidden -– forms of time scale separation.

I will explain some concepts from geometric singular perturbation theory and geometric desingularization based on the blow-up method in combination with standard techniques from dynamical systems theory which I use to understand the geometry of self-sustained (non-classical relaxation) oscillations.