Project summary

This ANR project, to start in April 2025, aims to investigate how the inherent heterogeneity of a population of interacting particles affects its capacity for self-organization, via the mathematical analysis of models for interacting particles, and an application to fish collective motion. Despite increasing experimental evidence that a biological system’s heterogeneity impacts its collective behavior, to this day few mathematical models for interacting particles take into account their non-exchangeable nature. To shed light on the role of heterogeneity in the formation of collective patterns, we propose to study the asymptotic behavior of solutions to PDE models for selforganization in heterogeneous populations. To bridge this macroscopic description with microscopic models of interacting systems, we will also contribute to the development of a novel framework for large-population limits of non-exchangeable particle systems. Simultaneously, we will investigate the impact of inter-individual heterogeneity on phase transition between swimming patterns in a population of gregarious fish in a lab environment, in collaboration with a team of physicists.

Team

The mathematicians:

• Benoît Bonnet-Weill, CNRS Researcher at Laboratoire des Signaux et Systèmes (L2S) based at École CentraleSupelec

• David Poyato, Postdoctoral Researcher at the University of Granada 

The physicists:

• Ramiro Godoy-Diana, CNRS Researcher at ESPCI Paris, PMMH Laboratory 

• Benjamin Thiria, Professor at ESPCI Paris, PMMH Laboratory