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Derivation of a Micro-Macro Link for Collective Decision-Making Systems
Uncover Network Features Based on Drift Measurements
Heiko Hamann1, Gabriele Valentini2, Yara Khaluf1, and Marco Dorigo2
1Department of Computer Science, University of Paderborn, Paderborn, Germany
heiko.hamann@uni-paderborn.de
yara.khaluf@uni-paderborn.de
2IRIDIA, Université Libre de Bruxelles, Brussels, Belgium
gvalenti@ulb.ac.be
mdorigo@ulb.ac.be
Abstract. Relating microscopic features (individual level) to macroscopic features (swarm level) of self-organizing collective systems is challenging. In this paper, we report the mathematical derivation of a macroscopic model starting from a microscopic one for the example of collective decision-making. The collective system is based on the application of a majority rule over groups of variable size which is modeled by chemical reactions (micro-model). From an approximated master equation we derive the drift term of a stochastic differential equation (macro-model) which is applied to predict the expected swarm behavior. We give a recursive definition of the polynomials defining this drift term. Our results are validated by Gillespie simulations and simulations of the locust alignment.
LNCS 8672, p. 181 ff.
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© Springer International Publishing Switzerland 2014