Pattern phase transitions in 3D minimal Vicsek model

¹ School of Artificial Intelligence and Automation, Key Laboratory of Image Processing and Intelligent Control, State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology Wuhan 430074, PRC
² Jiangsu Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University Nanjing 210096, PRC
³ Adaptive Networks and Control Lab, and Center of Smart Networks and Systems, School of Information Science and Engineering, Fudan University - Shanghai 200433, China

^(a) zht@mail.hust.edu.cn (corresponding author)

Received: 29 November 2020
Accepted: 8 April 2021

Abstract

A large part of biological collective behaviors involves motional formation patterns like migration, vortex, aggregation, etc., in three-dimensional space, but the phase transition principles among these patterns still remain a dilemma. In this letter, by tweaking the vision range of the particles in a minimal collective motion model, phase transitions are observed among gas-like, crystal-like, and liquid-sphere–like patterns. Significantly, the increase of noise magnitudes will destroy the moving direction synchronization of gas-like and crystal-like phases, but not the liquid-sphere–like phase. By contrast, three sub-phases of migration liquid-sphere, vortex liquid-sphere and aggregation liquid-sphere emerge by slightly increasing noise magnitudes. This study sheds some light onto the forming mechanisms of 3D motional patterns of abundant biological groups. These insights could be expected to enable tuning the collective motional formations of multi-unmanned systems or robots by simply tweaking a few dynamical parameters as well.