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

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.