Heterophilious Dynamics Enhances Consensus

By Sébastien Motsch, Eitan Tadmor. SIAM Review, 2013

582 citations recorded by the source corpus.

We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or “agents,” with the tendency to adjust to their “environmental averages.” This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of “rules of engagement” influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment in...

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6be34301023f77dcd4dc3b646e196823b2d39423

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Citations in the corpus

Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, background): “[15, 17, 27, 37, 40, 46, 50, 52]), stochastic terms ([18, 23, 25]), pedestrian crowds (see [16, 31]), infinite-dimensional kinetic models (see [1, 4, 9, 12, 22, 28, 49]), topological models ([5, 29]), control models (see [6, 10, 11, 43, 51]).”
Emergent dynamics of the Cucker-Smale flocking model and its variants (2016, background): “For other survey on the related topics, we refer to [14, 51].”
Mean-field and graph limits for collective dynamics models with time-varying weights (2020, background): “In this case, every agent can potentially interact with any other if the distance separating them belongs to the support of the interaction function a: there is no underlying network (see for instance [24]).”
Eulerian dynamics with a commutator forcing III. Fractional diffusion of order 0 (2017, methodology): “Starting with the seminal work of Cucker and Smale paper [4] and the follow-up works [7, 6, 10, 17, 2, 15] and reference therein, it has become clear that in order to achieve unconditional flocking in either the agent-based or the macroscopic descriptions (1.”
Long-Time Behaviour and Phase Transitions for the Mckean–Vlasov Equation on the Torus (2018, unknown): “We refer to [45,54,55,60] and the references therein for a comprehensive list of such models.”
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): “System (1) retains simple additive interactions, contrary to the more complex structure found for example in [71,72]; but it still includes a large range of first order models, such as swarming, opinion dynamics, aggregation equations, neuroscience models, see for instance [10,16,22,30] or [61] and ”
On the control through leadership of the Hegselmann–Krause opinion formation model (2015, unknown): “[26] for a survey.”
A tutorial on modeling and analysis of dynamic social networks. Part I (2017, background): “= X j s(xj −xi)(xj(t)−xi(t)) ∈ R, (31) where s : R → R+ stands for some even continuous function (similar multidimensional models, extending (19) to the case of continuous time, have been examined in [138, 139, 148]). Smoothed and discontinuous bounded conﬁdence models inherit many properties of the”
Clustering and asymptotic behavior in opinion formation (2014, background): “But this case was extensively studied in [19] and we recall one of the main result in this paper Theorem 5 (Motsch-Tadmor) There exists C and λ > 0 depending only on N and φ s.”