15,749 research outputs found
Opinion Dynamics in Social Networks with Hostile Camps: Consensus vs. Polarization
Most of the distributed protocols for multi-agent consensus assume that the
agents are mutually cooperative and "trustful," and so the couplings among the
agents bring the values of their states closer. Opinion dynamics in social
groups, however, require beyond these conventional models due to ubiquitous
competition and distrust between some pairs of agents, which are usually
characterized by repulsive couplings and may lead to clustering of the
opinions. A simple yet insightful model of opinion dynamics with both
attractive and repulsive couplings was proposed recently by C. Altafini, who
examined first-order consensus algorithms over static signed graphs. This
protocol establishes modulus consensus, where the opinions become the same in
modulus but may differ in signs. In this paper, we extend the modulus consensus
model to the case where the network topology is an arbitrary time-varying
signed graph and prove reaching modulus consensus under mild sufficient
conditions of uniform connectivity of the graph. For cut-balanced graphs, not
only sufficient, but also necessary conditions for modulus consensus are given.Comment: scheduled for publication in IEEE Transactions on Automatic Control,
2016, vol. 61, no. 7 (accepted in August 2015
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence
The problem of analyzing the performance of networked agents exchanging
evidence in a dynamic network has recently grown in importance. This problem
has relevance in signal and data fusion network applications and in studying
opinion and consensus dynamics in social networks. Due to its capability of
handling a wider variety of uncertainties and ambiguities associated with
evidence, we use the framework of Dempster-Shafer (DS) theory to capture the
opinion of an agent. We then examine the consensus among agents in dynamic
networks in which an agent can utilize either a cautious or receptive updating
strategy. In particular, we examine the case of bounded confidence updating
where an agent exchanges its opinion only with neighboring nodes possessing
'similar' evidence. In a fusion network, this captures the case in which nodes
only update their state based on evidence consistent with the node's own
evidence. In opinion dynamics, this captures the notions of Social Judgment
Theory (SJT) in which agents update their opinions only with other agents
possessing opinions closer to their own. Focusing on the two special DS
theoretic cases where an agent state is modeled as a Dirichlet body of evidence
and a probability mass function (p.m.f.), we utilize results from matrix
theory, graph theory, and networks to prove the existence of consensus agent
states in several time-varying network cases of interest. For example, we show
the existence of a consensus in which a subset of network nodes achieves a
consensus that is adopted by follower network nodes. Of particular interest is
the case of multiple opinion leaders, where we show that the agents do not
reach a consensus in general, but rather converge to 'opinion clusters'.
Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks,
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