Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Chaos: An Interdisciplinary Journal of Nonlinear Science Year : 2017

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.
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Dates and versions

hal-01412154 , version 1 (08-12-2016)

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Audric Drogoul, Romain Veltz. Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2017, ⟨10.1063/1.4976510⟩. ⟨hal-01412154⟩
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