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We propose a modified Vicsek-like model to study influence dynamics and opinion formation in social networks. We work on the premise that opinions of members of a group may be considered to be analogous to the direction of motion of a…
In this note we study a new kinetic model of opinion dynamics. The model incorporates two forces -- alignment of opinions under all-to-all communication driving the system to a consensus, and Rayleigh type friction force that drives each…
We consider the Hegselmann-Krause model for opinion dynamics and study the evolution of the system under various settings. We first analyze the termination time of the synchronous Hegselmann-Krause dynamics in arbitrary finite dimensions…
We study here the dynamics of opinion formation in a society where we take into account of the internally held beliefs and externally expressed opinions of the individuals, which are not necessarily the same at all times. While these two…
Considerable effort using techniques developed in statistical physics has been aimed at numerical simulations of agent-based opinion models and analysis of their results. Such work has elucidated how various rules for interacting agents can…
We consider the following distributed consensus problem: Each node in a complete communication network of size $n$ initially holds an \emph{opinion}, which is chosen arbitrarily from a finite set $\Sigma$. The system must converge toward a…
We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among…
We study a time-delayed variant of the Hegselmann-Krause opinion formation model featuring a small group of leaders and a large group of non-leaders. In this model, leaders influence all agents but only interact among themselves. At the…
The cognitive process of opinion formation is often characterized by stubbornness or resistance of agents to changes of opinion. To capture such a feature we introduce a constant latency time in the standard voter model of opinion dynamics:…
We study the dynamics of opinion formation in the situation where changing opinion involves a cost for the agents. To do so we couple the dynamics of a heterogeneous bounded confidence Hegselmann-Krause model with that of the resources that…
We study a nonlinear bounded-confidence model (BCM) of continuous-time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a scalar $\gamma$, which controls the steepness of a smooth…
Motivated by empirical research on bias and opinion formation, we formulate a multidimensional nonlinear opinion-dynamical model where agents have individual biases, which are fixed, as well as opinions, which evolve. The dimensions…
This study adopts a nonlinear dynamics approach, specifically using bifurcation theory, to analyze social interactions and behavior in online communities. Referencing key works by Steven Strogatz and others, the paper explores the…
Among the different disciplines in the social, behavioral and economic sciences, a fundamental class of problems is related to the prediction of the final state of the presence of individual opinions in a large population. The main aspects…
We present a model of opinion dynamics in which agents adjust continuous opinions as a result of random binary encounters whenever their difference in opinion is below a given threshold. High thresholds yield convergence of opinions towards…
Opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or non-periodic. At each time step, all agents…
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…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our…
Social consensus is important for society. Sometimes the success of society depends on a consensus (e.g. the decision to pay taxes or to commit to the constitution). Examples for continuous opinion dynamics are discussions about tax rates…