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arXiv · 2105.10597

Interacting Hawkes processes with multiplicative inhibition

Céline Duval·Eric Luçon·Christophe Pouzat
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Abstract

In the present work, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We give first a detailed analysis of the well-posedness of this interacting system as well as its dynamics in large population. The second aim of the paper is to give a rigorous analysis of the longtime behavior of the mean-field limit process. We provide also numerical evidence that inhibition and retroaction may be responsible for the emergence of limit cycles in such system.

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Céline Duval, Eric Luçon, Christophe Pouzat. 2021-05-21. Interacting Hawkes processes with multiplicative inhibition. https://arxiv.org/abs/2105.10597

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