Related papers: Hegselmann-Krause and Cucker-Smale type models wit…
Latane social impact theory predicts recruitment and supportive interactions being responsible for opinion formation. So far only recruitment interactions were considered in the voter models. Here we consider a noisy voter model with…
We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…
We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence…
We study emergent dynamics of the discrete Cucker-Smale (in short, DCS) model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient…
We study the large-time behavior of systems driven by radial potentials, which react to anticipated positions, ${\mathbf x}^\tau(t)={\mathbf x}(t)+\tau {\mathbf v}(t)$, with anticipation increment $\tau>0$. As a special case, such systems…
Inspired by the work of [Kempe, Kleinberg, Oren, Slivkins, EC13] we introduce and analyze a model on opinion formation; the update rule of our dynamics is a simplified version of that of Kempe et. al. We assume that the population is…
In this paper, we study the singular Cucker-Smale (C-S) model on the real line. For long range case, i.e. $\beta<1$, we prove the uniqueness of the solution in the sense of Definition 2.1 and the unconditional flocking emergence. Moreover,…
Over the past decade, contrary to the early popular expectation that large-scale discourse in online communities would foster greater consensus, the large-scale structure of online discourse has been measured to be strongly polarized.…
The original Hegselmann-Krause (HK) model consists of a set of~$n$ agents that are characterized by their opinion, a number in~$[0, 1]$. Each agent, say agent~$i$, updates its opinion~$x_i$ by taking the average opinion of all its…
People's opinions change with time as they interact with each other. In a bounded-confidence model (BCM) of opinion dynamics, individuals (which are represented by the nodes of a network) have continuous-valued opinions and are influenced…
We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a…
Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a…
Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…
Collective dynamics of many interacting particles have been widely studied because of a wealth of their behavioral patterns quite different from the individual traits. A selective way of birds that reacts to their neighbors is one of the…
The classic Hegselmann-Krause (HK) model for opinion dynam- ics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of all the agents within a fixed distance R. In this work, we…
A generalization of the Cucker-Smale model for collective animal behaviour is investigated. The model is formulated as a system of delayed stochastic differential equations. It incorporates two additional processes which are present in…
In the Deffuant model, individuals are located on the vertices of a graph, and are characterized by their opinion, a number in $[-1, 1]$. The dynamics depends on two parameters: a confidence threshold $\theta < 2$ and a convergent parameter…
We here propose a model to simulate the process of opinion formation, which accounts for the mutual affinity between interacting agents. Opinion and affinity evolve self-consistently, manifesting a highly non trivial interplay. A continuous…
In this short note we study what happens in a symmetric opinion model when we send the total interacting population $N(t)$ to infinity as $t \to \infty$. We assume that new population enters the system with opinions that are i.i.d random…
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…