A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations

Francesco Vecil (1) , Pauline Lafitte (2) , Jesus Rosado Linares (3)

1 UV - Universitat de València
2 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
3 Department of Mathematics [UCLA]

We study at particle and kinetic level a collective behavior model based on three phenomena: self-propulsion, friction (Rayleigh effect) and an attractive/repulsive (Morse) potential rescaled so that the total mass of the system remains constant independently of the number of particles N . In the first part of the paper, we introduce the particle model: the agents are numbered and described by their position and velocity. We iden- tify five parameters that govern the possible asymptotic states for this system (clumps, spheres, dispersion, mills, rigid-body rotation, flocks) and perform a numerical analysis on the 3D setting. Then, in the second part of the paper, we describe the kinetic system derived as the limit from the particle model as N tends to infinity; we propose, in 1D, a numerical scheme for the simulations, and perform a numerical analysis devoted to trying to recover asymptotically patterns similar to those emerging for the equivalent particle systems, when particles originally evolved on a circle.

Mots clés: swarming; self-organization; collective behavior; attractive/repulsive potential

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Francesco Vecil, Pauline Lafitte, Jesus Rosado Linares. A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations. Physica D: Nonlinear Phenomena, 2013, 10.1016/j.physd.2012.12.010. ⟨10.1016/j.physd.2012.12.010⟩. ⟨hal-00726486⟩