Lyapunov exponent in the Vicsek model

Abstract

The well-known Vicsek model describes the flock dynamics of self-propelled agents. Surprisingly, a direct measure of the chaotic behavior of such systems is missing. Here, we discuss the kinetic phase transition present in Vicsek systems in light of the largest Lyapunov exponent, which is numerically computed by following the dynamical evolution in tangent space. As discontinuities in the neighbors weighting factor hinder the computations, we propose a continuous form of the model. Our results about chaotic regime reinforce the idea that the Lyapunov exponent is also a phase transition indicator.Comment: 7 pages, 16 equations, 6 figure