Interacting Hawkes processes with multiplicative inhibition

Céline Duval, Eric Luçon and Christophe Pouzat

Stochastic Processes and their Applications, 2022, vol. 148, issue C, 180-226

Abstract: In the present work, we introduce a general class of mean-field interacting nonlinear Hawkes processes modeling 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.

Keywords: Multivariate nonlinear Hawkes processes; Inhibition; Mean-field systems; Neural networks (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:148:y:2022:i:c:p:180-226

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DOI: 10.1016/j.spa.2022.02.008

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