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Continuum Modeling of Biological Network Formation Read chapter Read first chapter

2017 | OriginalPaper | Chapter

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

Authors : Young-Pil Choi, Seung-Yeal Ha, Zhuchun Li

Published in: Active Particles, Volume 1

Publisher: 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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previous chapter A Review on Attractive–Repulsive Hydrodynamics for Consensus in Collective Behavior
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Metadata
Title
Emergent Dynamics of the Cucker–Smale Flocking Model and Its Variants
Authors
Young-Pil Choi
Seung-Yeal Ha
Zhuchun Li
Copyright Year
2017
Book
Active Particles, Volume 1

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

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

Copyright Year: 2017

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

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