# Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics

Abstract : In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived \cite{de_masi_hydrodynamic_2015,fournier_toy_2016} mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a recipe'' to find such bifurcation which nicely complements the works in Refs.~\onlinecite{de_masi_hydrodynamic_2015,fournier_toy_2016}. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
Type de document :
Article dans une revue
Chaos, American Institute of Physics, 2017, 〈10.1063/1.4976510〉

https://hal.inria.fr/hal-01412154
Contributeur : Romain Veltz <>
Soumis le : jeudi 8 décembre 2016 - 09:01:36
Dernière modification le : jeudi 11 janvier 2018 - 16:47:40

### Citation

Audric Drogoul, Romain Veltz. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics. Chaos, American Institute of Physics, 2017, 〈10.1063/1.4976510〉. 〈hal-01412154〉

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