Pattern Formation as a Transient Phenomenon in the Nonlinear Dynamics of a Multi-Agent System

Heiko Hamann
in Proc. of MATHMOD 2009 - 6th Vienna International Conference on Mathematical Modelling 6 (2009)


This paper presents a microscopic model (agent positions, directions, and interac-
tions are explicitly modeled) of mobile agents (or self-propelled particles) that is inspired by
the “complex transport networks” reported by [4]. Here, the agents’ positions are modeled con-
tinuously. 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 (dis-
crete 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 them-
selves (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. I empiri-
cally investigate the transient times in dependence of the system’s size and give examples.

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