Emergent dynamics of the cucker–Smale flocking model and its variants

Young Pil Choi; Seung Yeal Ha; Zhuchun Li

doi:10.1007/978-3-319-49996-3_8

Emergent dynamics of the cucker–Smale flocking model and its variants

Young Pil Choi, Seung Yeal Ha, Zhuchun Li

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

70 Citations (Scopus)

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.

Original language	English
Title of host publication	Modeling and Simulation in Science, Engineering and Technology
Publisher	Springer Basel
Pages	299-331
Number of pages	33
Edition	9783319499949
DOIs	https://doi.org/10.1007/978-3-319-49996-3_8
Publication status	Published - 2017

Publication series

Name	Modeling and Simulation in Science, Engineering and Technology
Number	9783319499949
ISSN (Print)	2164-3679
ISSN (Electronic)	2164-3725

Bibliographical note

Funding Information:
Acknowledgements The work of S.-Y. Ha was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03. The work of Y.-P. Choi was supported by Engineering and Physical Sciences Research Council (EP/K008404/1). The work of Z. Li was supported by the National Natural Science Foundation of China Grant No.11401135, and Fundamental Research Funds for the Central Universities (HIT.BRETIII.201501 and HIT.PIRS.201610).

Publisher Copyright:
© Springer International Publishing AG 2017.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Engineering(all)
Fluid Flow and Transfer Processes
Computational Mathematics

Access to Document

10.1007/978-3-319-49996-3_8

Fingerprint Dive into the research topics of 'Emergent dynamics of the cucker–Smale flocking model and its variants'. Together they form a unique fingerprint.

Cite this

@inbook{3e9076b1c9b44d13bfb9ae644f6b4872,

title = "Emergent dynamics of the cucker–Smale flocking model and its variants",

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{\textquoteright}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{\textquoteright}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.",

author = "Choi, {Young Pil} and Ha, {Seung Yeal} and Zhuchun Li",

note = "Funding Information: Acknowledgements The work of S.-Y. Ha was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03. The work of Y.-P. Choi was supported by Engineering and Physical Sciences Research Council (EP/K008404/1). The work of Z. Li was supported by the National Natural Science Foundation of China Grant No.11401135, and Fundamental Research Funds for the Central Universities (HIT.BRETIII.201501 and HIT.PIRS.201610). Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.",

year = "2017",

doi = "10.1007/978-3-319-49996-3_8",

language = "English",

series = "Modeling and Simulation in Science, Engineering and Technology",

publisher = "Springer Basel",

number = "9783319499949",

pages = "299--331",

booktitle = "Modeling and Simulation in Science, Engineering and Technology",

edition = "9783319499949",

}

Emergent dynamics of the cucker–Smale flocking model and its variants. / Choi, Young Pil; Ha, Seung Yeal; Li, Zhuchun.

Modeling and Simulation in Science, Engineering and Technology. 9783319499949. ed. Springer Basel, 2017. p. 299-331 (Modeling and Simulation in Science, Engineering and Technology; No. 9783319499949).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Emergent dynamics of the cucker–Smale flocking model and its variants

AU - Choi, Young Pil

AU - Ha, Seung Yeal

AU - Li, Zhuchun

N1 - Funding Information: Acknowledgements The work of S.-Y. Ha was supported by the Samsung Science and Technology Foundation under Project Number SSTF-BA1401-03. The work of Y.-P. Choi was supported by Engineering and Physical Sciences Research Council (EP/K008404/1). The work of Z. Li was supported by the National Natural Science Foundation of China Grant No.11401135, and Fundamental Research Funds for the Central Universities (HIT.BRETIII.201501 and HIT.PIRS.201610). Publisher Copyright: © Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85026319286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026319286&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-49996-3_8

DO - 10.1007/978-3-319-49996-3_8

M3 - Chapter

AN - SCOPUS:85026319286

T3 - Modeling and Simulation in Science, Engineering and Technology

SP - 299

EP - 331

BT - Modeling and Simulation in Science, Engineering and Technology

PB - Springer Basel

ER -

Emergent dynamics of the cucker–Smale flocking model and its variants

Abstract

Publication series

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this