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Time-variant feedback processes in collective decision-making systems: influence and effect of dynamic neighborhood sizes

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Abstract

Self-organizing systems rely on positive feedback (amplification of perturbations). In particular, in swarm systems, positive feedback builds up in a transient phase until maximal positive feedback is reached and the system converges temporarily on a state close to consensus. We investigate two examples of swarm systems showing time-variant positive feedback: alignment in locust swarms and adaptive aggregation of swarms. We identify an influencing bias in the spatial distribution of agents compared to a well-mixed distribution and two features, percentage of aligned swarm members and neighborhood size, that allow us to model the time variance of feedbacks. We report an urn model that is capable of qualitatively representing all these relevant features. The increase in neighborhood sizes over time enables the swarm to lock in a highly aligned state but also allows for infrequent switching between lock-in states. We report similar occurrences of time-variant feedback in a second collective system to indicate the potential for generality of this phenomenon. Our study is concluded by applications of methods from renormalization group theory that allow us to focus on the neighborhood dynamics as scale transformations. Correlation lengths and critical exponents are determined empirically.

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Notes

  1. Naturally, the definition of order is ambiguous. Here, we say that a uniform distribution of agents in space is an unordered state.

  2. A fly bottle is a traditional device made of clear glass to passively trap flying insects that enter it from below and cannot escape because of their phototaxis behavior.

  3. In terms of the actual implementation, real distances are represented by a fine-grained histogram.

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Acknowledgments

This work was partially supported by the European Research Council through the ERC Advanced Grant ‘E-SWARM: Engineering Swarm Intelligence Systems’ (Contract 246939) and the EU-H2020 project ‘florarobotica,’ No. 640959. Thanks to Yara Khaluf for helpful comments of an earlier version of this manuscript.

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Authors and Affiliations

  1. IRIDIA, Université Libre de Bruxelles, Brussels, Belgium

    Gabriele Valentini

  2. Department of Computer Science, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Heiko Hamann

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  1. Gabriele Valentini
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Correspondence to Heiko Hamann.

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Valentini, G., Hamann, H. Time-variant feedback processes in collective decision-making systems: influence and effect of dynamic neighborhood sizes. Swarm Intell 9, 153–176 (2015). https://doi.org/10.1007/s11721-015-0108-8

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