Emergence of multi-cluster configurations from attractive and repulsive interactions

Seung Yeal Ha; Eunhee Jeong; Jeong Han Kang; Kyungkeun Kang

doi:10.1142/S0218202512500133

Emergence of multi-cluster configurations from attractive and repulsive interactions

Seung Yeal Ha, Eunhee Jeong, Jeong Han Kang, Kyungkeun Kang

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

We discuss a first-order CuckerSmale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

Original language	English
Article number	12500133
Journal	Mathematical Models and Methods in Applied Sciences
Volume	22
Issue number	8
DOIs	https://doi.org/10.1142/S0218202512500133
Publication status	Published - 2012 Aug

Bibliographical note

Funding Information:
The work of S.-Y. Ha is partially supported by a National Research Foundation from Korea Grant funded by the Korean Government (2009-0093137) and a research grant of the College of Natural Sciences in SNU. K.K.’s work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692. J.K.’s work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-330-B00128).

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Applied Mathematics

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10.1142/S0218202512500133

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title = "Emergence of multi-cluster configurations from attractive and repulsive interactions",

abstract = "We discuss a first-order CuckerSmale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.",

author = "Ha, {Seung Yeal} and Eunhee Jeong and Kang, {Jeong Han} and Kyungkeun Kang",

note = "Funding Information: The work of S.-Y. Ha is partially supported by a National Research Foundation from Korea Grant funded by the Korean Government (2009-0093137) and a research grant of the College of Natural Sciences in SNU. K.K.{\textquoteright}s work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692. J.K.{\textquoteright}s work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-330-B00128).",

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AU - Ha, Seung Yeal

AU - Jeong, Eunhee

AU - Kang, Jeong Han

AU - Kang, Kyungkeun

N1 - Funding Information: The work of S.-Y. Ha is partially supported by a National Research Foundation from Korea Grant funded by the Korean Government (2009-0093137) and a research grant of the College of Natural Sciences in SNU. K.K.’s work was partially supported by KRF-2008-331-C00024 and NRF-2009-0088692. J.K.’s work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-330-B00128).

PY - 2012/8

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N2 - We discuss a first-order CuckerSmale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

AB - We discuss a first-order CuckerSmale-type consensus model with attractive and repulsive interactions and present upper and lower bound estimates on the number of asymptotic point-clusters depending on the relative ranges of interactions and coupling strength. When the number of agents approaches infinity, we introduce a scalar conservation law with a non-local flux for a macroscopic description. We show that the corresponding conservation law admits a classical solution for sufficiently smooth initial data, which illustrates the shock avoidance effect due to the non-locality of the interactions. We also study the dynamics of special Dirac-Comb-type solutions consisting of two and three point-clusters.

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Emergence of multi-cluster configurations from attractive and repulsive interactions

Abstract

Bibliographical note

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