Dynamical Behavior of a Colony Migration System: Do Colony Size and Quorum Threshold Affect Collective Decision?

Abstract

Social insects are ecologically and evolutionarily the most successful organisms on earth and can achieve robust collective behaviors through local interactions among group members. Colony migration has been considered as a leading example of collective decision making in social insects. In this paper, a piecewise colony migration system with recruitment switching is proposed to explore underlying mechanisms and synergistic effects of colony size and quorum on the outcomes of collective decision. The dynamical behavior of the nonsmooth system is studied, and sufficient conditions for the existence and stability of equilibrium are provided. The theoretical results suggest that large colonies are more likely to emigrate to a new site. More interesting findings include but are not limited to that (a) the system may exhibit oscillation when the colony size is below a critical level and (b) the system may also exhibit a bistable state, i.e., the colony migrates to a new site or the old nest depending on the initial size of recruiters. Bifurcation analysis shows that the variations of colony size and quorum threshold greatly impact the dynamics. The results suggest that it is important to distinguish between two populations of recruiters in modeling. This work may provide important insights on how simple and local interactions achieve the collective migrating activity in social insects.