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Transient behavior of gossip opinion dynamics with community structure
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). (Digital Futures)ORCID iD: 0000-0003-2641-2962
KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control). (Digital Futures)ORCID iD: 0000-0001-9940-5929
2024 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 164, article id 111627Article in journal (Refereed) Published
Abstract [en]

We study transient behavior of gossip opinion dynamics, in which agents randomly interact pairwise over a weighted graph with two communities. Edges within a community have identical weights different from edge weights between communities. We first derive an upper bound for the second moment of agent opinions. Using this result, we obtain upper bounds for probability that a large proportion of agents have opinions close to average opinions. The results imply a phase transition of transient behavior of the process: When edge weights within communities are larger than those between communities and those between regular and stubborn agents, most agents in the same community hold opinions close to the average opinion of that community with large probability, at an early stage of the process. However, if the difference between intra- and inter-community weights is small, most of the agents instead hold opinions close to everyone's average opinion at the early stage. In contrast, when the influence of stubborn agents is large, agent opinions settle quickly to steady state. We then conduct numerical experiments to validate the theoretical results. Different from traditional asymptotic analysis in most opinion dynamics literature, the paper characterizes the influence of stubborn agents and community structure on the initial phase of the opinion evolution.

Place, publisher, year, edition, pages
Elsevier BV , 2024. Vol. 164, article id 111627
Keywords [en]
Community structure, Gossip model, Opinion dynamics, Phase transition, Transient behavior
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-345729DOI: 10.1016/j.automatica.2024.111627ISI: 001224089400001Scopus ID: 2-s2.0-85189518224OAI: oai:DiVA.org:kth-345729DiVA, id: diva2:1852505
Note

QC 20240603

Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-06-03Bibliographically approved

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Xing, YuJohansson, Karl H.

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