Krause's model of opinion dynamics on isolated time scales

Abstract

Communicated by M. A. LachowiczWe analyze a bounded confidence model, introduced by Krause, on isolated time scales. In this model, each agent takes into account only the assessments of the agents whose opinions are not too far away from its own opinion. We show that the behavior of the model depends strongly on the graininess function : If takes values in the interval 0, 1, then our discrete time scale model behaves similarly to the classical one, but if takes values in 1, C1OE, then the model has different properties. Simulations are performed to validate the theoretical results.

Discrete leader‐following consensus

“…A consensus algorithm describes the information transfers between agents and varies depending on the application and the model. In the literature, many different consensus algorithms have been proposed; we can mention here those based on nearest-neighbor rules, 3,[8][9][10][11][12] bounded confidence, [13][14][15][16] or a virtual leader. [17][18][19] The virtual leader is a special agent whose motion is independent of all the other agents and thus is followed by all the other ones.…”

(CMMSE paper) A finite‐difference model for indoctrination dynamics

“…Opinions can be interpreted as assessments made by the agents about prices, levels of preference (or agreement) with political parties, or controversial topics. Polarization into opinion clusters or the arising of a consensus in a social group has become of great interest in political science, economics, sociology, and sociophysics; see the study of Girejko, Machado, Malinowska, and Martins . Of particular interest are the conditions that lead to the emergence of consensus, and the time required to its arising if it can be finally reached; see the study of Lu, Sun, and Liu .…”

“…Polarization into opinion clusters or the arising of a consensus in a social group has become of great interest in political science, economics, sociology, and sociophysics; see the study of Girejko, Machado, Malinowska, and Martins. 11 Of particular interest are the conditions that lead to the emergence of consensus, and the time required to its arising if it can be finally reached; see the study of Lu, Sun, and Liu. 12 For example, Medina, Macías, Gallegos, and Vargas 13 have studied the emergence of a consensus about three political options.…”

Non-invasive Control of the Fractional Hegselmann–Krause Type Model

“…positions, velocity, opinion) by interacting with their neighbours. Consensus algorithms are based on nearest-neighbour rules [6,7,10,21], bounded confidence [4,8,9,20] or a virtual leader [3,23,28]. The virtual leader is an agent whose motion is independent of all the other agents, and thus is followed by all the other ones.…”