On the Analysis of Collective Dynamics in Social Groups with Bees and Football Players as Case Studies

Abstract

Okinawa Institute of Science and Technology Graduate UniversityDoctor of PhilosophyThe main focus of this thesis is investigating the emergent effects observed in the collective dynamics of the honeybee hive. We use a previously acquired dataset of time-resolved trajectories of hundreds of bees inside the hive, recorded for multiple days and nights. In a series of papers, we study the temporal and spatial dynamics of the bee hive, uncovering scale-free correlations of occupancy fluctuations in both temporal and spatial domains. These observations indicate the proximity of the system to the second-order phase transition. Furthermore, we observe a non-trivial relationship between throughput and density, implying that the beehive undergoes a jamming transition. This finding is explored further by constructing a model of jamming in 2D using stochastic cellular automata and exploring how correlation length is dependent on the density. Additional insights are obtained by studying the properties of the functional network computed using correlations between the timeseries of individual bees. The supplementary project is centered on the study of the trajectories of professional football players from the Japanese football league. It has been found that statistical properties of trajectories of individual players’ are best described by the Lévy walk dynamics. Furthermore, we have found that these dynamics are preserved when centers of mass trajectories for each team are considered. However, the power-law distribution of step sizes which is indicative of the Lévy walk is reduced to the exponential when only the periods when players are in possession of the ball are considered. Based on these findings we hypothesize that players’ behavior is reminiscent of that of the foraging animals which resort to Lévy walk when resource distribution is sparse.doctoral thesi