Swarm Intelligence

, Volume 9, Issue 2–3, pp 153–176 | Cite as

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

  • Gabriele Valentini
  • Heiko Hamann


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.


Swarm system Feedbacks Opinion dynamics Renormalization group Graph theory 



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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.IRIDIAUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Department of Computer ScienceUniversity of PaderbornPaderbornGermany

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