152 research outputs found
Network Synchronization in a Noisy Environment with Time Delays: Fundamental Limits and Trade-Offs
We study the effects of nonzero time delays in stochastic synchronization
problems with linear couplings in an arbitrary network. Using the known exact
threshold value from the theory of differential equations with delays, we
provide the synchronizability threshold for an arbitrary network. Further, by
constructing the scaling theory of the underlying fluctuations, we establish
the absolute limit of synchronization efficiency in a noisy environment with
uniform time delays, i.e., the minimum attainable value of the width of the
synchronization landscape. Our results have also strong implications for
optimization and trade-offs in network synchronization with delays.Comment: 3 figure
Diffusion Processes on Power-Law Small-World Networks
We consider diffusion processes on power-law small-world networks in
different dimensions. In one dimension, we find a rich phase diagram, with
different transient and recurrent phases, including a critical line with
continuously varying exponents. The results were obtained using self-consistent
perturbation theory and can also be understood in terms of a scaling theory,
which provides a general framework for understanding processes on small-world
networks with different distributions of long-range links.Comment: 4 pages, 3 figures, added references, modified Fig. 2 with added data
(PRL, in press
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