Blanchet, Adrien and Degond, Pierre (2017) Kinetic models for topological nearest-neighbor interactions. IAST Working Paper, n. 17-65, Toulouse

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Abstract

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in [10]. The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments.

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• Kinetic models for topological nearest-neighbor interactions. (deposited 28 Mar 2017 15:47) [Currently Displayed]
  • Kinetic models for topological nearest-neighbor interactions. (deposited 13 Apr 2018 12:13)