Modeling selective local interactions with memory: Motion on a 2D lattice

Authored by Daniel Weinberg, Doron Levy

Date Published: 2014-06-15

DOI: 10.1016/j.physd.2014.04.001

Sponsors: United States National Science Foundation (NSF)

Platforms: NetLogo

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We consider a system of particles that simultaneously move on a two-dimensional periodic lattice at discrete times steps. Particles remember their last direction of movement and may either choose to continue moving in this direction, remain stationary, or move toward one of their neighbors. The form of motion is chosen based on predetermined stationary probabilities. Simulations of this model reveal a connection between these probabilities and the emerging patterns and size of aggregates. In addition, we develop a reaction-diffusion master equation from which we derive a system of ODEs describing the dynamics of the particles on the lattice. Simulations demonstrate that solutions of the ODEs may replicate the aggregation patterns produced by the stochastic particle model. We investigate conditions on the parameters that influence the locations at which particles prefer to aggregate. This work is a two-dimensional generalization of Galante and Levy (2012), in which the corresponding one-dimensional problem was studied. (C) 2014 Elsevier B.V. All rights reserved.

Tags

Agent-based models Group dynamics Reaction-diffusion master equation collective motion