113,683 research outputs found
Opinion dynamics: models, extensions and external effects
Recently, social phenomena have received a lot of attention not only from
social scientists, but also from physicists, mathematicians and computer
scientists, in the emerging interdisciplinary field of complex system science.
Opinion dynamics is one of the processes studied, since opinions are the
drivers of human behaviour, and play a crucial role in many global challenges
that our complex world and societies are facing: global financial crises,
global pandemics, growth of cities, urbanisation and migration patterns, and
last but not least important, climate change and environmental sustainability
and protection. Opinion formation is a complex process affected by the
interplay of different elements, including the individual predisposition, the
influence of positive and negative peer interaction (social networks playing a
crucial role in this respect), the information each individual is exposed to,
and many others. Several models inspired from those in use in physics have been
developed to encompass many of these elements, and to allow for the
identification of the mechanisms involved in the opinion formation process and
the understanding of their role, with the practical aim of simulating opinion
formation and spreading under various conditions. These modelling schemes range
from binary simple models such as the voter model, to multi-dimensional
continuous approaches. Here, we provide a review of recent methods, focusing on
models employing both peer interaction and external information, and
emphasising the role that less studied mechanisms, such as disagreement, has in
driving the opinion dynamics. [...]Comment: 42 pages, 6 figure
Consensus problems in networks of agents with switching topology and time-delays
In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results
Consensus formation on coevolving networks: groups' formation and structure
We study the effect of adaptivity on a social model of opinion dynamics and
consensus formation. We analyze how the adaptivity of the network of contacts
between agents to the underlying social dynamics affects the size and
topological properties of groups and the convergence time to the stable final
state. We find that, while on static networks these properties are determined
by percolation phenomena, on adaptive networks the rewiring process leads to
different behaviors: Adaptive rewiring fosters group formation by enhancing
communication between agents of similar opinion, though it also makes possible
the division of clusters. We show how the convergence time is determined by the
characteristic time of link rearrangement. We finally investigate how the
adaptivity yields nontrivial correlations between the internal topology and the
size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J.
Phys. A covering the "Complex Networks: from Biology to Information
Technology" conference (Pula, Italy, 2007
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
Time scale modeling for consensus in sparse directed networks with time-varying topologies
The paper considers the consensus problem in large networks represented by
time-varying directed graphs. A practical way of dealing with large-scale
networks is to reduce their dimension by collapsing the states of nodes
belonging to densely and intensively connected clusters into aggregate
variables. It will be shown that under suitable conditions, the states of the
agents in each cluster converge fast toward a local agreement. Local agreements
correspond to aggregate variables which slowly converge to consensus. Existing
results concerning the time-scale separation in large networks focus on fixed
and undirected graphs. The aim of this work is to extend these results to the
more general case of time-varying directed topologies. It is noteworthy that in
the fixed and undirected graph case the average of the states in each cluster
is time-invariant when neglecting the interactions between clusters. Therefore,
they are good candidates for the aggregate variables. This is no longer
possible here. Instead, we find suitable time-varying weights to compute the
aggregate variables as time-invariant weighted averages of the states in each
cluster. This allows to deal with the more challenging time-varying directed
graph case. We end up with a singularly perturbed system which is analyzed by
using the tools of two time-scales averaging which seem appropriate to this
system
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