"Vicsek-Kuramoto system in collective dynamics and their macroscopic equations"Moschella, CarmelaIn this talk I consider an Individual-Based Model for self-propelled particles interacting through local alignment and investigate its macroscopic limit. This model has been first introduced by C. Chen et al. to describe the behaviour of dense colony of flagellated bacteria (e.g. Escherichia coli ) which self organize into robust collective oscillatory motion. In view of this, a ’Vicsek-Kuramoto style’ model has been used. In fact the agent based model combines both Kuramoto and Vicsek dynamics - it takes from Kuramoto model the way in which agents try to syncronize the phase of their rotational movement and from the Vicsek model the fact that the syncronization is spacially local. We study the mean-field and hydrodynamic limits of this system. Furthermore, we present numerical simulations of the microscopic system to illustrate the diverse collective behaviors exhibited by the model under different parameter values. |
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