A DISCRETE NONLINEAR AND NON–AUTONOMOUS MODEL OF CONSENSUS FORMATION

By Ulrich Krause. 2007

439 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ac29870217d17589e3ecfb9a94d965ebd7231567

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In Statistical and Nonlinear Physics

Citations in the corpus

Heterophilious Dynamics Enhances Consensus (2013, methodology): “7) in its (1)-dual form for column-stochastic matrices goes back to Dobrushin [46], and his so-called coefficient of ergodicity, η A , was later used to quantify the relative entropy in discrete Markov processes [29, 30] and the contractivity in models of opinion dynamics [75].”
Clustering and asymptotic behavior in opinion formation (2014, methodology): “Discretizing the equation with an explicit Euler method and a time step ∆t = 1 yields the so-called Krause model [14]: xn+1 i = ∑ j φ n ijx n j ∑ j φ n ij , φij = φ(|xj − xi |2).”
On Krause's Multi-Agent Consensus Model With State-Dependent Connectivity (2008, background): “It has however been observed in the literature that the distances between clusters are usually significantly larger than 1 (see [21], [24], and Fig.”
Continuous Opinion Dynamics under Bounded Confidence: A Survey (2007, methodology): “In recent years two models of genuinely continuous opinion dynamics under bounded conﬁdence have raised the interest of the sociophysics community: the models of Hegselmann and Krause (6; 7; 8) and Deﬀuant, Weisbuch and others (9; 10).”
Opinion Fluctuations and Disagreement in Social Networks (2010, neutral): “This mechanism was first proposed by Axelrod [5] in the discrete opinion dynamics setting, and then by Krause [30], and Deffuant and Weisbuch [18], in the continuous opinion dynamics framework.”
A review of the mean field limits for Vlasov equations (2014, neutral): “This is a time continuous variant, derived in [128], of the so-called Krause model, [111], [89] (see also the review [158]).”
Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2017, background): “1) retains simple additive interactions, contrary to the more complex structure found for example in [40, 41]; but it still includes a large range of first order models, such as swarming, opinion dynamics or aggregation equations, see for instance [2, 5, 10, 13] or [32].”
Opinion Dynamics and Learning in Social Networks (2011, methodology): “…by Clifford and Sud-bury [23] and by Holley and Liggett [60]), or continuous values (as in the DeGroot model [28] and the bounded conﬁdence models of Krause [63] (further developed by Hegselmann and Krause [59], Deffuant, Neau, Amblard and Weisbuch [27] and Weisbuch, Kirman and Herreiner [93])).”
A stabilization theorem for dynamics of continuous opinions (2005, background): “2) is a more dimensional version of the well known shrinking lemma, seen for example in [7].”
A tutorial on modeling and analysis of dynamic social networks. Part I (2017, methodology): “nﬁdence models stipulate that individuals are totally insensitive to opinions, falling outside their conﬁdence sets. A simple yet instructive models of this type were independently proposed by Krause [117] and Deﬀuant and Weisbuch [118]. The Deﬀuant-Weisbuch model, based on the idea of gossiping, wi”
Mean-field and graph limits for collective dynamics models with time-varying weights (2020, methodology): “In turn, the agents’ weights are assumed to evolve in time and their dynamics may depend on the opinions and weights of all the other agents, via functions ψ weights, the evolution of the opinions and weights are given by the following system: supplemented by the initial conditions We point out that”