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Unpublished Paper
Limitations and tradeoffs in synchronization of large-scale networks with uncertain links
Scientific Reports
  • Amit Diwadkar, Iowa State University
  • Umesh Vaidya, Iowa State University
Document Type
Article
Publication Date
4-1-2016
DOI
10.1038/srep21157
Abstract
The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scalar nonlinear systems with stochastic linear interactions over large-scale networks. This sufficient condition, expressed in terms of nonlinear dynamics, the Laplacian eigenvalues of the nominal interconnections, and the variance and location of the stochastic uncertainty, allows us to define a synchronization margin. We provide an analytical characterization of important trade-offs between the internal nonlinear dynamics, network topology, and uncertainty in synchronization. For nearest neighbour networks, the existence of an optimal number of neighbours with a maximum synchronization margin is demonstrated. An analytical formula for the optimal gain that produces the maximum synchronization margin allows us to compare the synchronization properties of various complex network topologies.
Comments

This article is from Scientific Reports 6 (2016): 21157, doi: 10.1038/srep21157. Posted with permission.

Rights
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
Copyright Owner
Macmillan Publishers Limited.
Language
en
File Format
application/pdf
Citation Information
Amit Diwadkar and Umesh Vaidya. "Limitations and tradeoffs in synchronization of large-scale networks with uncertain links" Scientific Reports Vol. 6 (2016) p. 21157 -1 - 21157-11
Available at: http://works.bepress.com/umesh-vaidya/1/