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A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions

Quentin Cormier 1
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : We consider a stochastic network of Integrate-and-Fire spiking neurons, in its mean-field asymptotic. Given an invariant probability measure of the McKean-Vlasov equation, we give a sufficient condition to ensure the local stability of this invariant measure. Our criteria involves the location of the zeros of an explicit holomorphic function associated to the considered invariant probability measure. We prove that when all the complex zeros have negative real part, local stability holds.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02488915
Contributor : Quentin Cormier <>
Submitted on : Monday, February 24, 2020 - 9:40:34 AM
Last modification on : Tuesday, May 18, 2021 - 2:32:02 PM

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  • HAL Id : hal-02488915, version 1
  • ARXIV : 2002.08649

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Quentin Cormier. A mean-field model of Integrate-and-Fire neurons: non-linear stability of the stationary solutions. 2020. ⟨hal-02488915⟩

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