论文标题
Vicsek模型中的Lyapunov指数
Lyapunov exponent in the Vicsek model
论文作者
论文摘要
众所周知的Vicsek模型描述了一群自propelled颗粒（SPP）的动力学。令人惊讶的是，没有直接衡量此类系统的混乱行为。在这里，我们根据最大的Lyapunov指数（LLE）讨论了Vicsek系统中存在的动态相变，该指数通过遵循最高200万属的切线空间的动态演化来计算。由于邻居加权因子的不连续性阻碍了计算，因此我们提出了Vicsek模型的平滑形式。我们发现基于LLE的SPP的集体行为的混乱制度。 LLE与用作控制参数的应用噪声的依赖性在Vicsek模型的众所周知过渡点附近明显变化。
The well-known Vicsek model describes the dynamics of a flock of self-propelled particles (SPPs). Surprisingly, there is no direct measure of the chaotic behavior of such systems. Here, we discuss the dynamical phase transition present in Vicsek systems in light of the largest Lyapunov exponent (LLE), which is numerically computed by following the dynamical evolution in tangent space for up to two million SPPs. As discontinuities in the neighbor weighting factor hinder the computations, we propose a smooth form of the Vicsek model. We find a chaotic regime for the collective behavior of the SPPs based on the LLE. The dependence of LLE with the applied noise, used as a control parameter, changes sensibly in the vicinity of the well-known transition points of the Vicsek model.
