A simple proof of the Cucker-Smale flocking dynamics and mean-field limit

By Seung‐Yeal Ha, Jian‐Guo Liu. 2009

600 citations recorded by the source corpus.

Subfields: Mathematical Physics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fd3a75af7ec5540c503010e72b9c8a9dd45f87cc

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Citations in the corpus

Mean Field Analysis of Controlled Cucker-Smale Type Flocking: Linear Analysis and Perturbation Equations (2011, methodology): “There are two main classes of models for the flocking and swarming behaviour: (i) individual based models in the form of coupled Ordinary (Stochastic) Differential Equations (O(S)DEs) (see for instance (Cucker and Smale, 2007)), and (ii) continuum models in the form of Partial (or integro-partial) D”
A General Collision-Avoiding Flocking Framework (2011, methodology): “The proof rests on ideas coming from [6] as well as on the beautiful method developed in [10].”
On the control through leadership of the Hegselmann–Krause opinion formation model (2015, unknown): “[1, 8, 6, 5, 10, 11, 12, 13, 15, 19], see also Ref.”
The derivation of swarming models: Mean-field limit and Wasserstein distances (2013, methodology): “, We refer to [34 46, 45, 26] for further discussion about this model and qualitative properties.”
Avoiding Collisions in Flocks (2010, methodology): “Extensions of these proofs in several directions can be found in [ 11 ], [12], [18].”
Flocking and asymptotic velocity of the Cucker–Smale model with processing delay (2014, methodology): “See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/260559300 Flocking and asymptotic velocity of the Cucker–Smale model with processing delay ARTICLE in JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS · JULY 2014 Impact Factor: 1.12 · DOI: ”
A New Model for Self-organized Dynamics and Its Flocking Behavior (2011, methodology): “We apply the energy method introduced by Ha and Liu [14].”
Heterophilious Dynamics Enhances Consensus (2013, methodology): “9 recovers the unconditional flocking results for the C-S model, φ(r) ∝ (1 + r)−2β , β > 1/2, obtained elsewhere in using spectral analysis, 1-, 2-, and ∞-based estimates [36, 61, 17, 60, 21].”
A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems (2018, unknown): “Besides, several prominent papers aimed at describing the emergence of patterns which were initially discovered for systems of ODEs in the context of kinetic models described by continuity equations [22, 38].”
Flocking estimates for the Cucker–Smale model with time lag and hierarchical leadership (2017, methodology): “To do this, we combine arguments used to deal with the undelayed models in both standard CS-system [26] and CS-system with hierarchical leadership [46].”
Emergent dynamics of the Cucker-Smale flocking model and its variants (2016, methodology): “[8, 41] Given f0 ∈ M(R 2d) compactly supported, take a sequence of μ0 of measures of the form:”