Flocking Regimes in a Simple Lattice Model

TL;DR

This paper introduces a one-dimensional lattice model that incorporates alignment, centring, and separation to study different flocking behaviors, supported by numerical simulations and mean-field analysis.

Contribution

It generalizes previous flocking models by including all three criteria and explores multiple flocking regimes through numerical and theoretical methods.

Findings

Identification of distinct flocking regimes: alternating, homogeneous, and dipole structures.

Numerical and mean-field analysis of regime stability and transitions.

Insights into microscopic rules leading to emergent collective behavior.

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.