The brain activity is the paradigmatic example of the dynamics of an extremely complex network of networks, where large heterogeneous neural populations interact over different time and spatial scales. A first step in the simplification of this dynamics amounts to reproducing the neural population dynamics at a mean field level and this has led to the development of neural mass and neural field models of increasing complexity.
One of the principal aims and challenges of these mean field approaches is to simplify the complexity of the system, using a reduced number of equations to describe the self-emergent dynamics, but still retaining the most relevant microscopic neuronal features at the level of the macroscopic description put forward. Various approaches have been developed in this context, mostly heuristic ones and it is only in the last years that rigourous methods, borrowed from nonlinear dynamics, statistical physics and the theory of large deviations have begun to be applied in this context.
Recent advances on the study of coupled phase oscillators based on the Ott-Antonsen ansatz have allowed to reduce the evolution of in-principle infinite dimensional systems to the dynamics of a limited number of macroscopic variables. This exact reduction methodology has been recently applied to neural spiking networks leading to the development of an extremely active research field aiming to develop a new generation of neural mass models.
The aim of this minisymposium is to gather experts from mathematics, statistical physics, nonlinear dynamics and neuroscience to present the very recent developments in the field and to discuss of possible cross-fertilization from one field to the other one.
Simona Olmi (Inria Sophia Antipolis Méditerranée Research Centre, Valbonne, France)
Alessandro Torcini (Laboratoire de Physique Theorique et Modelisation, CY Cergy Paris University, France)