Modeling the honeybee social network

     Collective behaviors emerging in many-body systems such as superfluidity have been the major interest of condensed matter physics community. The study of emergent phenomena is also applicable to social systems, as the interaction among members of a community would bring about collective properties such as generalized rigidity. However, it is still not clear what would be an appropriate order parameter characterizing a “community.” The overall goal of my research is to establish what is the analogue of generalized rigidity for communities.

    Honeybees are a well-known example of social animals. Since they are easier to experimentally manipulate than humans, researches on social dynamics are often conducted with these social insects. The time series of interactions among bees show the temporal network whose structure gives rise to interesting features of the social system. Previous experiments on honeybees in our group, in collaboration with Professor Gene Robinson of the University of Illinois, measured the duration time of interaction among the bees and the waiting time between two consecutive interactions. The distributions for these two times turned out to follow a power-law. The SocioPatterns data on human face-to-face interactions showed the same power-law for both interaction duration times and inter-event waiting times, which suggests that the heavy-tailed time distribution regarding interactions is universal among social systems. Starting from this observation, I am modeling the social network of honeybees using both computational and analytical tools. It is widely accepted that heterogeneity among agents is responsible for the dynamics observed in experiments and simulations. Therefore, I built a system where random “spin” directions are assigned to each random-walking agent and agents of similar spin values are more likely to have lasting interaction. Alignment of spins occur during interaction, resulting in local clusters of the same spins. My agent-based modeling reproduced the power-law time distributions exhibited in both honeybee and human interactions, and suggested different phases of this many-body system. More recently, I have been building and solving the stochastic differential equations to analytically derive the power-laws and phase diagram to understand the dynamics behind it.

What is the analogue of generalized rigidity for communities?