3 research outputs found
Lyapunov exponent in the Vicsek model
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
Contribution of individual degrees of freedom to Lyapunov vectors in many-body systems
International audienceWe use the weight δI, deduced from the estimation of Lyapunov vectors, in order to characterise regions in the kinetic (x, v) space with particles that most contribute to chaoticity. For the paradigmatic model, the cosine Hamiltonian mean field model, we show that this diagnostic highlights the vicinity of the separatrix, even when the latter hardly exists