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Models of continuous opinion dynamics under bounded confidence show a sharp transition between a consensus and a polarization phase at a critical global bound of confidence. In this paper, heterogeneous bounds of confidence are studied. The…
Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in…
The Sznajd cellular automata corresponds to one of the simplest and yet most interesting models of complex systems. While the traditional two-dimensional Sznajd model tends to a consensus state (pro or cons), the assignment of the contrary…
Geometric realization of opinion is considered as a simplex and the opinion space of a group of individuals is a simplicial complex whose topological features are monitored in the process of opinion formation. The agents are physically…
Recently, an opinion dynamics model has been proposed to describe a network of individuals discussing a set of logically interdependent topics. For each individual, the set of topics and the logical interdependencies between the topics…
Bounded confidence models of opinion dynamics have been actively studied in recent years, in particular, opinion formation and extremism propagation along with other aspects of social dynamics. In this work, after an analysis of limitations…
A model to describe the spontaneous formation of military and economic coalitions among a group of countries is proposed using spin glass theory. Between each couple of countries, there exists a bond exchange coupling which is either zero,…
Adaptive models of opinion formation among humans can display a fragmentation transition, where a social network breaks into disconnected components. Here, we investigate this transition in a class of models with arbitrary number of…
Among the several approaches that have been attempted at studying opinion dynamics, the Sznajd model provides some particularly interesting features, such as its simplicity and ability to represent some of the mechanisms believed to be…
The dynamical process of opinion formation within a model using a local majority opinion updating rule is studied numerically in networks with the small-world geometrical property. The network is one in which shortcuts are added to randomly…
Recent formulation of the Zaller model of mass opinion is generalized to include the interaction between agents. The mechanism of interaction is close to the bounded confidence model. The outcome of the simulation is the probability…
We study multidimensional continuous opinion dynamics, where opinions are nonnegative vectors which components sum up to one. Examples of such opinions are budgets or other allocation vectors which display a distribution of a fixed amount…
In recent years, opinion dynamics has received an increasing attention, and various models have been introduced and evaluated mainly by simulation. In this study, we introduce and study a dynamical model inspired by the so-called `bounded…
We investigate majority rule dynamics in a population with two classes of people, each with two opinion states $\pm 1$, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the…
The original Hegselmann-Krause (HK) model comprises a set of $n$ agents characterized by their opinion, a number in $[0,1]$. Agent $i$ updates its opinion $x_i$ via taking the average opinion of its neighbors whose opinion differs by at…
We present a renormalization approach to solve the Sznajd opinion formation model on complex networks. For the case of two opinions, we present an expression of the probability of reaching consensus for a given opinion as a function of the…
We present an extensive study of the joint effects of heterogeneous social agents and their heterogeneous social links in a bounded confidence opinion dynamics model. The full phase diagram of the model is explored for two different…
The formation of large social groups having uniform opinions influenced by mass media is currently an important topic in the social sciences. In this work, we explore and extend an off-lattice, two-dimensional Potts model (Eur. Phys. J. B…
We add a rejection mechanism (negative influence) into a two-dimensions bounded confidence model. The principle is that one shifts aways from a close attitude of one's interlocutor, when there is a strong disagreement on the other attitude.…
Politics around the world exhibits increasing polarization, demonstrated in part by rigid voting configurations in institutions like legislatures or courts. A crux of polarization is separation along a unidimensional ideological axis, but…