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.
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Hamann, H., Valentini, G., Khaluf, Y., Dorigo, M. (2014). Derivation of a Micro-Macro Link for Collective Decision-Making Systems. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_18
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DOI: https://doi.org/10.1007/978-3-319-10762-2_18
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10761-5
Online ISBN: 978-3-319-10762-2
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