Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 22, Issue 8, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202512500133
Keywords
Agent-based model; attraction; clustering; kinetic model; opinion formations; repulsion
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Funding
- National Research Foundation from Korea
- Korean Government [2009-0093137, NRF-2010-330-B00128, KRF-2008-331-C00024, NRF-2009-0088692]
- College of Natural Sciences in SNU
- National Research Foundation of Korea
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We discuss a first-order Cucker-Smale-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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