title: Extreme fluctuations in stochastic network coordination with time delays.
abstract: We study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks. We obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network. We then obtain the scaling behavior of the extreme fluctuations with system size, as well as the distribution of the extremes on complex networks, and compare them to those on regular one-dimensional lattices. For large complex networks, when the delay is not too close to the critical one, fluctuations at the nodes effectively decouple, and the limit distributions converge to the Fisher-Tippett-Gumbel density. In contrast, fluctuations in low-dimensional spatial graphs are strongly correlated, and the limit distribution of the extremes is the Airy density. Finally, we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes.
authors.affiliation: Department of Physics, Applied Physics, and Astronomy.|Network Science and Technology Center.
authors.forename: D
authors.initials: D
authors.lastname: Hunt
authors.affiliation: Department of Physics, Applied Physics, and Astronomy.|Network Science and Technology Center.
authors.forename: F
authors.initials: F
authors.lastname: Molnár
authors.affiliation: Network Science and Technology Center.|Department of Computer Science Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
authors.forename: B K
authors.initials: BK
authors.lastname: Szymanski
authors.affiliation: Department of Physics, Applied Physics, and Astronomy.|Network Science and Technology Center.
authors.forename: G
authors.initials: G
authors.lastname: Korniss