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Emergent Behaviors over Signed Random Dynamical Networks: state-flipping model
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2015 (English)In: IEEE Transactions on Control of Network Systems, ISSN 2325-5870, Vol. 2, no 2, 142-153 p.Article in journal (Refereed) Published
Abstract [en]

Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/ inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to these recommendations. Conditions for almost sure convergence and divergence of the node states are established. We show that under this so-called state-flipping model, all links contribute to a consensus of the absolute values of the nodes, even under switching sign patterns and dynamically changing environment. A no-survivor property is established, indicating that every node state diverges almost surely if the maximum network state diverges.

Place, publisher, year, edition, pages
IEEE , 2015. Vol. 2, no 2, 142-153 p.
Keyword [en]
Consensus dynamics, random graphs, signed networks
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-165967DOI: 10.1109/TCNS.2014.2378915ISI: 000365085700005Scopus ID: 2-s2.0-84933049766OAI: oai:DiVA.org:kth-165967DiVA: diva2:809216
Note

QC 20151215

Available from: 2015-04-30 Created: 2015-04-30 Last updated: 2015-12-15Bibliographically approved

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Johansson, Karl Henrik

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