Flip motion of solitary wave in an Ising-type Vicsek model

Abstract

An Ising-type Vicsek model is proposed for collective motion and sudden direction change in a population of self-propelled particles. Particles move on a linear lattice with velocity +1 or −1 in the one-dimensional model. The probability of the velocity of a particle at the next step is determined by the number difference of the right-and left-moving particles at the present lattice site and its nearest-neighboring sites. A solitary wave appears also in our model similarly to previous models. In some parameter range, the moving direction of the solitary wave sometimes changes rather suddenly, which is like the sudden change of moving direction of a flock of birds. We study the average reversal time of traveling direction numerically and compare the results with a mean-field theory. The onedimensional model is generalized to a two-dimensional model. Flip motion of a bandlike soliton is observed in the two-dimensional model.