title: Synchrony in stochastically driven neuronal networks with complex topologies.
abstract: We study the synchronization of a stochastically driven, current-based, integrate-and-fire neuronal model on a preferential-attachment network with scale-free characteristics and high clustering. The synchrony is induced by cascading total firing events where every neuron in the network fires at the same instant of time. We show that in the regime where the system remains in this highly synchronous state, the firing rate of the network is completely independent of the synaptic coupling, and depends solely on the external drive. On the other hand, the ability for the network to maintain synchrony depends on a balance between the fluctuations of the external input and the synaptic coupling strength. In order to accurately predict the probability of repeated cascading total firing events, we go beyond mean-field and treelike approximations and conduct a detailed second-order calculation taking into account local clustering. Our explicit analytical results are shown to give excellent agreement with direct numerical simulations for the particular preferential-attachment network model investigated.
authors.affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3250, USA.
authors.forename: Katherine A
authors.initials: KA
authors.lastname: Newhall
authors.affiliation: Department of Physics and Astronomy, Iowa State University, 12 Physics Hall, Ames, Iowa 50011-3160, USA.
authors.forename: Maxim S
authors.initials: MS
authors.lastname: Shkarayev
authors.affiliation: Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
authors.forename: Peter R
authors.initials: PR
authors.lastname: Kramer
authors.affiliation: Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
authors.forename: Gregor
authors.initials: G
authors.lastname: Kovačič
authors.affiliation: Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, 251 Mercer Street, New York, New York 10012, USA.|Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Dong Chuan Road 800, Shanghai 200240, China.|NYUAD Institute, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates.
authors.forename: David
authors.initials: D
authors.lastname: Cai
mesh_terms: D008959:Models, Neurological; D009415:Nerve Net / Q000166:cytology*; D009474:Neurons / Q000166:cytology*; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors