Collective Dynamics in Biological and Social Systems

Modeling Selective Local Interactions with Memory

Doron Levy

University of Maryland

Motivated by phototaxis, we consider a system of particles that simultaneously move on 1D or 2D 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. Our results demonstrate a connection between these probabilities and the emerging patterns and size of aggregates. We develop a reaction diffusion master equation from which we derive a system of ODEs describing the dynamics of the particles on the lattice. We show that the ODEs may replicate the aggregation patterns produced by the stochastic particle model. This is a joint work with Amanda Galante and Dan Weinberg.