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Self-organized pattern formation in a swarm system as a transient phenomenon of non-linear dynamics

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  • Heiko Hamann
  • Thomas Schmickl
  • Karl Crailsheim

Abstract

This article presents a microscopic model (agent positions, directions and interactions are explicitly modelled) of mobile agents (or self-propelled particles) that is inspired by the ‘complex transport networks’ reported by Jones (2010; The emergence and dynamical evolution of complex transport networks from simple low-level behaviours , International Journal of Unconventional Computing 6, pp. 125--144). Here, the agents' positions are modelled continuously. This multi-agent system (or artificial swarm) shows a wide variety of self-organized pattern formations. The self-organization is based on the non-linearity 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 behaviour is relevant. We empirically investigate the transient times in dependence of several system parameters and give examples.

Suggested Citation

  • Heiko Hamann & Thomas Schmickl & Karl Crailsheim, 2011. "Self-organized pattern formation in a swarm system as a transient phenomenon of non-linear dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 18(1), pages 39-50, May.
    • Handle: RePEc:taf:nmcmxx:v:18:y:2011:i:1:p:39-50
    DOI: 10.1080/13873954.2011.601418
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    1. Troy Shinbrot, 2005. "Drat such custard!," Nature, Nature, vol. 438(7070), pages 922-923, December.
    2. Eric Bonabeau & Guy Theraulaz & Vincent Fourcassi'e & Jean-Louis Deneubourg, 1998. "The Phase-Ordering Kinetics of Cemetery Organization in Ants," Working Papers 98-01-008, Santa Fe Institute.
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