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Chin. Phys. B, 2021, Vol. 30(12): 128703    DOI: 10.1088/1674-1056/ac3c3f

Discontinuous and continuous transitions of collective behaviors in living systems

Xu Li(李旭)1,2,†, Tingting Xue(薛婷婷)1,†, Yu Sun(孙宇)2, Jingfang Fan(樊京芳)1,2, Hui Li(李辉)1,2, Maoxin Liu(刘卯鑫)3, Zhangang Han(韩战钢)1, Zengru Di(狄增如)1,2, and Xiaosong Chen(陈晓松)1,2,‡
1 School of Systems Science, Beijing Normal University, Beijing 100878, China;
2 Institute of Nonequilibrium Systems, Beijing Normal University, Beijing 100878, China;
3 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
Abstract  Living systems are full of astonishing diversity and complexity of life. Despite differences in the length scales and cognitive abilities of these systems, collective motion of large groups of individuals can emerge. It is of great importance to seek for the fundamental principles of collective motion, such as phase transitions and their natures. Via an eigen microstate approach, we have found a discontinuous transition of density and a continuous transition of velocity in the Vicsek models of collective motion, which are identified by the finite-size scaling form of order-parameter. At strong noise, living systems behave like gas. With the decrease of noise, the interactions between the particles of a living system become stronger and make them come closer. The living system experiences then a discontinuous gas-liquid like transition of density. The even stronger interactions at smaller noise make the velocity directions of the particles become ordered and there is a continuous phase transition of collective motion in addition.
Keywords:  living systems      phase emergence      phase transitions      eigen mircostate  
Received:  16 November 2021      Revised:  22 November 2021      Accepted manuscript online:  23 November 2021
PACS:  87.10.-e (General theory and mathematical aspects)  
  05.70.Fh (Phase transitions: general studies)  
  64.60.Ht (Dynamic critical phenomena)  
  89.75.-k (Complex systems)  
Fund: Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A10) and the National Natural Science Foundation of China (Grant No. 71731002).
Corresponding Authors:  Xiaosong Chen     E-mail:

Cite this article: 

Xu Li(李旭), Tingting Xue(薛婷婷), Yu Sun(孙宇), Jingfang Fan(樊京芳), Hui Li(李辉), Maoxin Liu(刘卯鑫), Zhangang Han(韩战钢), Zengru Di(狄增如), and Xiaosong Chen(陈晓松) Discontinuous and continuous transitions of collective behaviors in living systems 2021 Chin. Phys. B 30 128703

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