10,184 research outputs found
Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions
In this work we study the coupled dynamics of social balance and opinion
formation. We propose a model where agents form opinions under bounded
confidence, but only considering the opinions of their friends. The signs of
social ties -friendships and enmities- evolve seeking for social balance,
taking into account how similar agents' opinions are. We consider both the case
where opinions have one and two dimensions. We find that our dynamics produces
the segregation of agents into two cliques, with the opinions of agents in one
clique differing from those in the other. Depending on the level of bounded
confidence, the dynamics can produce either consensus of opinions within each
clique or the coexistence of several opinion clusters in a clique. For the
uni-dimensional case, the opinions in one clique are all below the opinions in
the other clique, hence defining a "left clique" and a "right clique". In the
two-dimensional case, our numerical results suggest that the two cliques are
separated by a hyperplane in the opinion space. We also show that the
phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and
Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the
context of politics, we comment about the possible relation of our results to
the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201
Partial containment control over signed graphs
In this paper, we deal with the containment control problem in presence of
antagonistic interactions. In particular, we focus on the cases in which it is
not possible to contain the entire network due to a constrained number of
control signals. In this scenario, we study the problem of selecting the nodes
where control signals have to be injected to maximize the number of contained
nodes. Leveraging graph condensations, we find a suboptimal and computationally
efficient solution to this problem, which can be implemented by solving an
integer linear problem. The effectiveness of the selection strategy is
illustrated through representative simulations.Comment: 6 pages, 3 figures, accepted for presentation at the 2019 European
Control Conference (ECC19), Naples, Ital
Intrinsic Reduced Attitude Formation with Ring Inter-Agent Graph
This paper investigates the reduced attitude formation control problem for a
group of rigid-body agents using feedback based on relative attitude
information. Under both undirected and directed cycle graph topologies, it is
shown that reversing the sign of a classic consensus protocol yields
asymptotical convergence to formations whose shape depends on the parity of the
group size. Specifically, in the case of even parity the reduced attitudes
converge asymptotically to a pair of antipodal points and distribute
equidistantly on a great circle in the case of odd parity. Moreover, when the
inter-agent graph is an undirected ring, the desired formation is shown to be
achieved from almost all initial states
Differential Inequalities in Multi-Agent Coordination and Opinion Dynamics Modeling
Distributed algorithms of multi-agent coordination have attracted substantial
attention from the research community; the simplest and most thoroughly studied
of them are consensus protocols in the form of differential or difference
equations over general time-varying weighted graphs. These graphs are usually
characterized algebraically by their associated Laplacian matrices. Network
algorithms with similar algebraic graph theoretic structures, called being of
Laplacian-type in this paper, also arise in other related multi-agent control
problems, such as aggregation and containment control, target surrounding,
distributed optimization and modeling of opinion evolution in social groups. In
spite of their similarities, each of such algorithms has often been studied
using separate mathematical techniques. In this paper, a novel approach is
offered, allowing a unified and elegant way to examine many Laplacian-type
algorithms for multi-agent coordination. This approach is based on the analysis
of some differential or difference inequalities that have to be satisfied by
the some "outputs" of the agents (e.g. the distances to the desired set in
aggregation problems). Although such inequalities may have many unbounded
solutions, under natural graphic connectivity conditions all their bounded
solutions converge (and even reach consensus), entailing the convergence of the
corresponding distributed algorithms. In the theory of differential equations
the absence of bounded non-convergent solutions is referred to as the
equation's dichotomy. In this paper, we establish the dichotomy criteria of
Laplacian-type differential and difference inequalities and show that these
criteria enable one to extend a number of recent results, concerned with
Laplacian-type algorithms for multi-agent coordination and modeling opinion
formation in social groups.Comment: accepted to Automatic
Emergent Behaviors over Signed Random Networks in Dynamical Environments
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. Positive
recommendations follow the standard consensus update while two types of
negative recommendations, each modeling a different type of antagonistic or
malicious interaction, are considered. Nodes may weigh positive and negative
recommendations differently, and random processes are introduced to model the
time-varying attention that nodes pay to the positive and negative
recommendations. Various conditions for almost sure convergence, divergence,
and clustering of the node states are established. Some fundamental
similarities and differences are established for the two notions of negative
recommendations
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
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