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Résumé |
The celebrated Ott-Antonsen ansatz for coupled oscillators provides a useful framework for working with deterministic systems in the thermodynamic limit, but it fails to capture many features of stochastic systems.
Several solutions have been recently proposed to accurately describe the behaviour of the order parameters in coupled oscillator systems. However, a fluctuating description of the order parameters at the mesoscopic scale was missing. In this talk, I will show how to derive an exact fluctuating theory for systems of coupled oscillators and its implications for theoretical neuroscience, from individual neurons to whole-brain neural mass models.
The theory allows one to derive Langevin equations for the order parameters, opening the door to study features of synchronisation phase transitions and finite-size effects.
In particular, I will show a novel application for quadratic integrate-and-fire (QIF) neurons. The QIF model has become an extremely powerful tool in computational neuroscience since its publication in 2015, leading to the so-called "next-generation" neural field models. However, it was limited to deterministic systems. I will present a fully stochastic version of the macroscopic description of the QIF neurons. |
