Is there a trade-off between simplicity and robustness? Illustration on a lattice-gas model of swarming

Abstract : We re-visit in detail a cellular automaton rule that was proposed some twenty years ago to explain the formation of swarms of particles: under some conditions, particles that are initially randomly scattered on a lattice may form coherent groups and move in a common direction, decided by a form of consensus. Our study focuses on the model introduced by A. Deutsch. The interactions between particles are local and stochastic: the particles tend to align with the neighbouring particles according to a single parameter, called the alignment sensitivity. Observations show the presence of a " minimal cohesion force " : the particles self-organise into patterns only when the alignment sensitivity is set higher than a threshold which depends on the number of particles in the grid. If this sensitivity is too low, no pattern emerges. When it becomes sufficiently high, it was observed that a spontaneous symmetry breaking occurs: the particles form a stripe pattern that moves diagonally on the lattice; the direction it takes results from a distributed consensus between particles. The purpose of this book chapter is to explore the various behaviours of the model and see how they depend on the sensitivity and on the density. In a second time, we ask if this behaviour resist various modifications of the model or if its simple and discrete nature make it sensitive to such modifications.
Type de document :
Pré-publication, Document de travail
TO APPEAR in 2018 in a monography with ISBN 978-3-319-65556-7. 2018
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Soumis le : lundi 29 février 2016 - 16:52:11
Dernière modification le : jeudi 11 janvier 2018 - 06:25:24
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Distributed under a Creative Commons Paternité - Pas d'utilisation commerciale 4.0 International License

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  • HAL Id : hal-01230145, version 1

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Nazim Fatès, Vincent Chevrier, Olivier Bouré. Is there a trade-off between simplicity and robustness? Illustration on a lattice-gas model of swarming. TO APPEAR in 2018 in a monography with ISBN 978-3-319-65556-7. 2018. 〈hal-01230145〉

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