Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

TY - JOUR

T1 - Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

AU - Fretter, Christoph

AU - Lesne, Annick

AU - Hilgetag, Claus C

AU - Hütt, Marc-Thorsten

PY - 2017/2/10

Y1 - 2017/2/10

N2 - 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.

AB - 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.

KW - Journal Article

U2 - 10.1038/srep42340

DO - 10.1038/srep42340

M3 - SCORING: Journal article

C2 - 28186182

VL - 7

SP - 42340

JO - SCI REP-UK

JF - SCI REP-UK

SN - 2045-2322

ER -