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We study the signum consensus protocol in continuous-time systems over arbitrary weighted directed graphs with bounded disturbances. The right-hand side of the differential equation is discontinuous on a codimension-$n$ manifold ($n > 1$).…
The voter model on networks is crucial to understand opinion formation. Uni-directional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model on a…
We study a distributed consensus problem on a complete communication network of $n$ vertices, each holding one of two opinions. The vertices communicate in rounds, possibly in the presence of adversarial noise, and exchange information…
In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, is especially important. Linear graph-based dynamics and bounded confidence dynamics are the two most popular…
This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of…
Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1].…
In this work, we study the consensus problem in which legitimate agents send their values over an undirected communication network in the presence of an unknown subset of malicious or faulty agents. In contrast to former works, we…
For a group of autonomous communicating agents, the ability to distinguish a meaningful input from disturbance, and come to collective agreement or disagreement in response to that input, is paramount for carrying out coordinated…
Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse…
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…
In this technical note, we first clarify a technical issue in the convergence proof of a free-will arbitrary time (FwAT) consensus law proposed recently in Pal et al. IEEE Trans. Cybern. (2020)[1], making the results questionable. We then…
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation…
We introduce a DeGroot-based model for opinion dynamics in social networks. A community of agents is represented as a weighted directed graph whose edges indicate how much agents influence one another. The model is formalized using labeled…
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter $k \ge 0$, in addition to its $+$ or $-$ opinion state. The evolution of the…
Bounded confidence opinion dynamics model the propagation of information in social networks. However in the existing literature, opinions are only viewed as abstract quantities without semantics rather than as part of a decision-making…
Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level…
Opinion dynamics aims to understand how individuals' opinions evolve through local interactions. Recently, opinion dynamics have been modeled as network games, where individuals update their opinions in order to minimize the social pressure…
Far beyond its relevance for commercial and political marketings, opinion formation and decision making processes are central for representative democracy, government functioning, and state organization. In the present report, a stochastic…
We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of…
The focus of this work is on designing influencing strategies to shape the collective opinion of a network of individuals. We consider a variant of the voter model where opinions evolve in one of two ways. In the absence of external…