Max-Olivier Hongler

Swarms Dynamics: Analytically Soluble Models of Agents Collective Behaviours in Random Environments

Swarms of flocking birds, schools of fishes and similar collective evolutions are due to specific mutual interactions which connect the agents forming large societies. A natural mathematical approach to stylize such types of flocking phenomena is to study the behaviour of the set of solutions of large systems of stochastic differential equations. As actual societies of agents may be either homogeneous, (agents are indistinguishable) or heterogeneous, (a small subgroup of agent act differently), the suitable mathematical frameworks will obviously also differ accordingly. In the seminar, I intend to construct analytically soluble models of swarm dynamics for both homo- and heterogeneous situations. These exactly soluble models explicitly unveil how, by suitable tuning external control parameters, mutual interactions enable to bifurcate from individual fully disorganised behaviours to stable collective spatio-temporal evolutions. Mean-field games and feedback particles filters are some recent mathematical tools which enter into the proposed mathematical modelling.