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Social insects are ecologically and evolutionarily most successful organismson earth, which can achieve robust collective behaviors through localinteractions among group members. Colony migration has been considered as aleading example of collective decision-making in social insects. In this paper,a piecewise colony migration system with recruitment switching is proposed toexplore underlying mechanisms and synergistic effects of colony size and quorumon the outcomes of collective decision. The completed dynamical analysis forthe non-smooth system (including the dynamics on subsystems, switching surface,and full system) is performed, and the sufficient conditions significantlyrelated to colony size for the stability of equilibria are provided. Thetheoretical results suggest that large colonies are more likely to emigrate toa new site. More interesting findings include but not limit to: (a) the systemmay exhibit oscillation when the colony size is below a critical level; (b) thesystem may also exhibit a bistable state, and colonies migrate to a new site orthe old nest depending on their initial sizes of recruiters. Bifurcationanalysis shows that the variations of colony size and quorum threshold greatlyimpact the dynamics. The results suggest that it is important to distinguishtwo populations of recruiters in modeling. This work may provide importantinsights on how simple and local interactions achieve the collective migratingactivity in social insects.

Dynamical behavior of a colony migration system: Do colony size and quorum threshold affect collective-decision?