Order-Disorder Oscillations in the Populations of Faulty Repulsive Agents

Abstract

We study the temporal evolution of populations including thousands of mobile repulsive agents. In the first part, the agents follow the rules of a deterministic automaton. We show that, the population may evolve toward different types of high-symmetry steady distributions, depending on the agent-agent repulsion law, and on the presence (or absence) of borders around the playground. We observe the formation of hexagonal-condensed lattices that maximize the potential function of the agent distribution. In the second part, agents are faulty. They violate the repulsion law and follow the rule of a non-deterministic automaton. We observe fast and random oscillations between the ordered phase and a strongly disorganized state when the number of agents is small (say for population involving a few tens of agents). These oscillations are essentially averaged and disappear in the large populations, resulting in a partially-ordered homogeneous distribution