Emergence of multi-cluster configurations from attractive and repulsive interactions

SY Ha, E Jeong, JH Kang, K Kang - Mathematical Models and …, 2012 - World Scientific
SY Ha, E Jeong, JH Kang, K Kang
Mathematical Models and Methods in Applied Sciences, 2012World Scientific
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 …
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.
World Scientific
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