Section: Application Domains

Neurosciences

Cortical networks are constituted of a large number of statistically similar neurons in interaction. Each neuron has a nonlinear dynamics and is subject to noise. Moreover, neurological treatment involve several timescales. Multiscale analysis, both in spatial (number of cells) and temporal hence also constitute mathematical foundations of our approaches to neurosciences. In addition to the techniques described in section 3.1 - 3.4, our approach of the activity of large cortical areas involve:

• limit theorems of stochastic interacting particles systems, such as coupling methods or large deviations techniques, as used in mathematical approaches to the statistical physics of gases

• bifurcation analysis of deterministic and stochastic differential equations used to analyse the qualitative behaviour of networks

• singular perturbation theory, geometrical and topological approaches in dynamical systems used to uncover the dynamics in the presence of multiple timescales.