title: Network coordination and synchronization in a noisy environment with time delays.
abstract: We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in complex networks. We consider two types of time delays: transmission delays between interacting nodes and local delays at each node (due to processing, cognitive, or execution delays). By investigating the underlying fluctuations for several delay schemes, we obtain the synchronizability threshold (phase boundary) and the scaling behavior of the width of the synchronization landscape, in some cases for arbitrary networks and in others for specific weighted networks. Numerical computations allow the behavior of these networks to be explored when direct analytical results are not available. We comment on the implications of these findings for simple locally or globally weighted network couplings and possible trade-offs present in such systems.
authors.affiliation: Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
authors.forename: D
authors.initials: D
authors.lastname: Hunt
authors.forename: B K
authors.initials: BK
authors.lastname: Szymanski
authors.forename: G
authors.initials: G
authors.lastname: Korniss
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D015233:Models, Statistical