Multiscale models in mathematical biology and neurosciences (R-2073)

The project deals with the study of multiple-scale phenomena in life sciences, more particularly in mathematical biology and neurology. A number of biological processes occur on a hierarchy of fundamentally different scales, be it in space or time. In the human body, for example, cells aggregate to form tissues, which in turn are contained in organs that build up the organism, resulting in a range of scales from micro to macro. Similarly, processes such as protein synthesis occur on vastly different time scales, with transcription of DNA into RNA being the fast process, whereas translation of RNA to amino acids is typically much slower, leading to a two time-scale structure. Mathematically, such processes can be modeled using multiple-scale, or fast-slow, systems of ordinary differential equations. We will focus on the mathematics of mixed-mode oscillations, i.e. dynamics that is characterized by time series in which large-amplitude spikes alternate with small-amplitude oscillations.

Keywords:DYNAMICAL SYSTEMS, Mathematical biology, Mixed-mode oscillations, Multi-timescale models, Singular perturbations

Disciplines:Mathematical sciences and statistics