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Erschienen in:
Continuum Modeling of Biological Network Formation Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants

verfasst von : Young-Pil Choi, Seung-Yeal Ha, Zhuchun Li

Erschienen in: Active Particles, Volume 1

Verlag: Springer International Publishing

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Abstract

In this chapter, we present the Cucker–Smale-type flocking models and discuss their mathematical structures and flocking theorems in terms of coupling strength, interaction topologies, and initial data. In 2007, two mathematicians Felipe Cucker and Steve Smale introduced a second-order particle model which resembles Newton’s equations in N-body system and present how their simple model can exhibit emergent flocking behavior under sufficient conditions expressed only in terms of parameters and initial data. After Cucker–Smale’s seminal works in [31, 32], their model has received lots of attention from applied math and control engineering communities. We discuss the state of the art for the flocking theorems to Cucker–Smale-type flocking models.

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Vorheriges Kapitel A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior
Nächstes Kapitel Follow-the-Leader Approximations of Macroscopic Models for Vehicular and Pedestrian Flows
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Metadaten
Titel
Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants
verfasst von
Young-Pil Choi
Seung-Yeal Ha
Zhuchun Li
Copyright-Jahr
2017
Buch
Active Particles, Volume 1

Print ISBN: 978-3-319-49994-9

Electronic ISBN: 978-3-319-49996-3

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-49996-3_8

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