Extreme value theory of evolving phenomena in complex dynamical systems: Firing cascades in a model of a neural network - Équipe Systèmes dynamiques : théories et applications Accéder directement au contenu
Article Dans Une Revue Chaos: An Interdisciplinary Journal of Nonlinear Science Année : 2020

Extreme value theory of evolving phenomena in complex dynamical systems: Firing cascades in a model of a neural network

Résumé

We extend the scope of the dynamical theory of extreme values to cover phenomena that do not happen instantaneously, but evolve over a finite, albeit unknown at the onset, time interval. We consider complex dynamical systems, composed of many individual subsystems linked by a network of interactions. As a specific example of the general theory, a model of neural network, introduced to describe the electrical activity of the cerebral cortex, is analyzed in detail: on the basis of this analysis we propose a novel definition of neuronal cascade, a physiological phenomenon of primary importance. We derive extreme value laws for the statistics of these cascades, both from the point of view of exceedances (that satisfy critical scaling theory) and of block maxima.

Dates et versions

hal-03120054 , version 1 (25-01-2021)

Identifiants

Citer

Theophile Caby, Giorgio Mantica. Extreme value theory of evolving phenomena in complex dynamical systems: Firing cascades in a model of a neural network. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020, 30 (4), pp.043118. ⟨10.1063/1.5120570⟩. ⟨hal-03120054⟩
48 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More