Flocking Regimes in a Simple Lattice Model

Abstract

We study a one-dimensional lattice flocking model incorporating all three of the flocking criteria proposed by Reynolds [Computer Graphics vol.21 4 (1987)]: alignment, centring and separation. The model generalises that introduced by O. J. O' Loan and M. R. Evans [J. Phys. A. vol. 32 L99 (1999)]. We motivate the dynamical rules by microscopic sampling considerations. The model exhibits various flocking regimes: the alternating flock, the homogeneous flock and dipole structures. We investigate these regimes numerically and within a continuum mean-field theory.