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Mercredi 17 mars

14h00 – 15h00, online-for link write to Annalisa Panati

Mean field models for fluctuation driven population dynamics

Matteo di Volo (LPTM, Université de Cergy-Pontoise)

Lorentzian distributions (LD) have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. However, due to the divergence of all the conventional moments and cumulants it is not possible to go beyond the ideal case, even for slight deformations of the LD due to noise sources. We will discuss a reduction method to analytically
investigate heterogenous systems with perturbed LD by considering an expansion of the characteristic function in terms of ’pseudo-cumulants’.
In particular, this approach allows to derive low dimensional mean field models for the macroscopic evolution of heterogeneous spiking networks of quadratic integrate-and-fire
neurons subject to extrinsinc and endogenous random fluctuations. Finally, the mean field model will be employed to describe collective oscillations measured in the Hippocampus with macroscopic recordings.

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