Kinetic models for topological nearest-neighbor interactions

Blanchet, Adrien and Degond, Pierre (2017) Kinetic models for topological nearest-neighbor interactions. TSE Working Paper, n. 17-786, Toulouse

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Official URL: http://tse-fr.eu/pub/31577

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.

Item Type: Monograph (Working Paper)
Language: English
Date: March 2017
Place of Publication: Toulouse
Uncontrolled Keywords: rank-based interaction, spatial diffusion equation, continuity equation, concentration of measure
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 24 Mar 2017 13:40
Last Modified: 21 Mar 2018 14:40
OAI ID: oai:tse-fr.eu:31577
URI: http://publications.ut-capitole.fr/id/eprint/23264

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