title: Topological effects on dynamics in complex pulse-coupled networks of integrate-and-fire type.
abstract: For a class of integrate-and-fire, pulse-coupled networks with complex topology, we study the dependence of the pulse rate on the underlying architectural connectivity statistics. We derive the distribution of the pulse rate from this dependence and determine when the underlying scale-free architectural connectivity gives rise to a scale-free pulse-rate distribution. We identify the scaling of the pairwise coupling between the dynamical units in this network class that keeps their pulse rates bounded in the infinite-network limit. In the process, we determine the connectivity statistics for a specific scale-free network grown by preferential attachment.
authors.affiliation: Mathematical Sciences Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA.
authors.forename: Maxim S
authors.initials: MS
authors.lastname: Shkarayev
authors.forename: Gregor
authors.initials: G
authors.lastname: Kovačič
authors.forename: David
authors.initials: D
authors.lastname: Cai
mesh_terms: D008962:Models, Theoretical; D013997:Time Factors