Journal of Statistical Physics

, Volume 170, Issue 4, pp 800–808 | Cite as

Stimulus Sensitivity of a Spiking Neural Network Model



Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been used to model spiking neural networks. Using mean-field approximation, the response of the network to a stimulus is computed and we provide a notion of stimulus sensitivity. It appears that the maximal sensitivity is achieved in the sub-critical regime, yet almost critical for a range of biologically relevant parameters.


Transmission of information Criticality Hawkes process Time elapsed equation 

Mathematics Subject Classification

60K35 92B20 82B27 



The author would like to thank Eva Löcherbach for inspiring discussions on this topic. This research was supported by the project Labex MME-DII (ANR11-LBX-0023-01) and mainly conducted during the stay of the author at Université de Cergy-Pontoise.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.AGM (UMR-CNRS 808), Université de Cergy-PontoiseCergy-PontoiseFrance
  2. 2.Univ. Grenoble Alpes, CNRS, LJKGrenobleFrance

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