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

Young Pil Choi, Seung Yeal Ha, Zhuchun Li

Research output: Chapter in Book/Report/Conference proceedingChapter

77 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 languageEnglish
Title of host publicationModeling and Simulation in Science, Engineering and Technology
PublisherSpringer Basel
Pages299-331
Number of pages33
Edition9783319499949
DOIs
Publication statusPublished - 2017

Publication series

NameModeling and Simulation in Science, Engineering and Technology
Number9783319499949
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

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