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.
|Journal||Mathematical Models and Methods in Applied Sciences|
|Publication status||Published - 2012 Aug|
Bibliographical noteFunding 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