中文摘要：

影响细胞群体行为的因素是多种多样的，除了以前研究的细胞通讯方式和环境因素外，还与现有文献没有或很少研究的细胞数目（即系统规模）有关．本文研究了系统规模对一类合成多细胞通讯系统的聚类行为的影响．在该系统中，单个系统是由压制振动子和基于延迟的松弛振子整合而成的振子，而振子之间通过群体感应机制相互耦合．通过分岔分析和数值模拟发现：细胞数目的增加不仅可以改变平衡态聚类稳定性区间的大小并诱导新的聚类行为，而且有利于扩大平衡态聚类的吸引域，表明细胞分化可能与系统规模有密切关系；细胞数目的增加还可以极大地丰富平衡态聚类和振动聚类的表现形式和共存方式，为生物体对环境的适应性提供了良好的基础．我们的结果不仅扩充了耦合系统的动力学行为，也为理解多细胞现象奠定了基础．

英文摘要：

There are many factors to influence the population behavior of cells. Except for the ways of cellular communication and the cellular environment, Which have been considered in the previous studies, the number of cells （or system size） that has been little considered before is also an important factor. This article investigates effects of system size on clustering behavior in a synthetic multicellular system, where individual oscillators are an integration of repressilator and hysteresis-based oscillators and are coupled through a quorum-sensing mechanism. By bifurcation analysis and numerical simulation, we find that increasing the cell number not only can change the size of the stability interval of steady state clusters and induce new clustering behaviors, but also benefits the enlargement of the attraction basin of steady state clusters, implying that cell differentiation may be closely related to the system size. In addition, such an increase can greatly extend the kinds and coexisting modes of steady state and oscillatory clusters, which would provide a good basis for the adaptability of organisms to the environment. Our results have extended the connotation of dynamics of coupled systems and also may be the foundation for understanding multicellular phenomena.