Motional9/9/2023 Series of interesting phenomena are observed including traveling bands 25, moving crystals 26, Swirlonic state 27, phase transition 28, 29, 30 and circular pattern 31, 32. Because the Vicsek model is simple but catches the main factors of collective motion, many researchers have paid attention to it in theory as well as simulation 20, 21, 22, 23, 24. Spontaneously local 18 and global velocity alignment 19 also be explored. Flocking phenomena is observed when the noise is small, which means the motion of all the agents almost reach global alignment and the degree of motional consensus is high. It considers the velocity alignment and noise for updating the velocity of all of the particles. The Vicsek model 17, proposed in 1995, is one of the classical models for studying collective motion of active systems. In addition, the study of motional consensus inspires the control of multibody systems such as a number of robotic machines 15, which is beneficial to exploring efficient motion strategies for escaping from fire etc 16. Studying the motional consensus of collective behavior is of great importance in discovering the basic principle of collective motion, which enables us to better understand the mechanism of escaping from predators, foraging etc 13, 14. Our results may be useful and encourage further efforts in exploring the basic principles of collective motion.Ĭollective behavior extensively exists in both the macroscopic systems such as the crowds of human 1, the herds of mammal 2, the flocks of bird 3, 4, 5, 6, the schools of fish 7 and the swarms of insect 8 and the microscopic systems including bacterial colonies, cells etc 9, 10, 11, 12. The variation of the effect of noise on motional consensus is non-monotonic for the change of the probability distribution of noise from uniform to non-uniform. In the cases with noise, we quantify the competition between velocity alignment and noise by considering the difference of the variety of order parameter result from the velocity alignment and noise. It is found that the weaker correlation of velocity leads to larger degree of aggregation of the particles. In the absence of noise, we propose a simple method, using grid-based technique and defining the normalized variance of the ratio of the number of particles locally to globally, to quantitatively study the movement pattern of the system by the spatial distribution of the particles and the degree of aggregation of particles. The motional consensus of self-propelled particles is studied in both noise-free cases and cases with noise by the standard Vicsek model.
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