Self-Organized Pattern Formation in a Swarm System as a Transient Phenomenon of Nonlinear Dynamics

Heiko Hamann, Thomas Schmickl, Karl Crailsheim
Mathematical and Computer Modelling of Dynamical Systems 18(1) (2012), 39-50

Abstract:

  This paper presents a microscopic model (agent positions,
  directions, and interactions are explicitly modeled) of mobile
  agents (or self-propelled particles) that is inspired by the
  ``complex transport networks'' reported by
  Jones, 2009. Here, the agents' positions are modeled
  continuously. This multi-agent system (or artificial swarm) shows a
  wide variety of self-organized pattern formations. The
  self-organization is based on the nonlinearity of the agents' turns
  (discrete jumps in the agents' directions) and the indirect
  interactions of the agents via a potential field that determines
  their motion (high values are attractive) and which is changed by
  themselves (agents increase the value of the potential field at
  their positions). At least most of the irregular and complex
  patterns are transient. The patterns found during the transient are
  more complex than those the system converges to. Still, this
  transient behavior is relevant. We empirically investigate the
  transient times in dependence of several system parameters and give
  examples.