Social insects are ecologically and evolutionarily most successful organisms on earth, which 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 non-smooth system is studied, and the 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 not limit to: (a) the system may exhibit oscillation when the colony size is below a critical level; (b) the system may also exhibit a bistable state, i.e., the colony migrates to a new site or the old nest depending on their initial sizes 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. This is a joint work with Lisha Wang, Takao Sasaki and Yun Kang.
邱志鹏，南京理工大学江阴校区基础前沿交叉中心主任、教授、博士生导师。主要从事常微分方程、动力系统与生物数学的研究工作，正在或完成主持国家自然科学基金4项，国家自然科学基金国际合作基金1项，教育部留学回国基金1项，参加国家自然科学基金面上项目2项和江苏省自然科学基金青年项目1项，目前已在Bull. Math. Biol., Math. Biosci., J. Diff. Equs., SIAM J. Appl. Math., J. Math. Biol., J. Theor. Biol., J. Math. Anal. Appl.等期刊上发表论文50余篇，曾先后访问过美国Purdue大学、Florida大学，意大利Trento大学、加拿大York大学和Alberta大学。
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