THE DENSITY IMPACT ON THE MATHEMATICAL MODEL OF THE SELF-PROPELLED PARTICLES IN THE HETEROGENEOUS MEDIA

Abstract

The collective dynamics of the self-driven particles was investigated mathematically and computationally. A two-dimension square shaped heterogeneous medium with boundaries  was developed to study the behavior of the self-propelled particles in the existence of the static obstacles. It was examined that how changes in density  impact on the collective motion of the SPP’s within the Heterogeneous media. The maximum cohesive motion and ferromagnetic alignment of the particles was determined in the presence of optimal noise . It was observed that as the number of the particles was increased, exceptional collective alignments among the particles were formed. At  and  an uninterrupted continuous escalation in motion was identified and the value of collective motion of self-propelled particles was reached at  out of  at  time steps. The inherited order parameter among the particles in this model is an important critical factor.