title: Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs.
abstract: Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.
authors.affiliation: Department of Life Sciences and Chemistry, Jacobs University Bremen, D-28759 Bremen, Germany.|Department of Computational Neuroscience, Universitätsklinikum Hamburg-Eppendorf, D-20246 Hamburg, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Fretter
authors.affiliation: LPTMC, CNRS, UMR 7600, UPMC-Paris 6, Sorbonne Universités, 4 place Jussieu, F-75252, Paris, France.|Institut de Génétique Moléculaire de Montpellier, UMR 5535 CNRS, 1919 route de Mende, 34293 Montpellier cedex 5, France; Université de Montpellier, 163 rue Auguste Broussonnet, 34090 Montpellier, France.
authors.forename: Annick
authors.initials: A
authors.lastname: Lesne
authors.affiliation: Department of Computational Neuroscience, Universitätsklinikum Hamburg-Eppendorf, D-20246 Hamburg, Germany.|Department of Health Sciences, Boston University, Boston, USA.
authors.forename: Claus C
authors.initials: CC
authors.lastname: Hilgetag
authors.affiliation: Department of Life Sciences and Chemistry, Jacobs University Bremen, D-28759 Bremen, Germany.
authors.forename: Marc-Thorsten
authors.initials: MT
authors.lastname: Hütt