The Vicsek model is a flocking model comprising simple point particles originally proposed with metric interactions: particles align to neighbours within a radius. Later, topological interactions were introduced such that particles align with their closest $k$ neighbours. We simulate the Vicsek model utilising topological neighbour interactions and estimate information theoretic quantities as a function of noise, the variability in the extent to which each particle aligns with its neighbours, and the flock direction. These quantities have been shown to be important in characterising phases transitions, such as that exhibited by the Vicsek model. We show that these quantities, mutual information and global transfer entropy, are in fact dependent on observation time, and in comparison to the canonical Vicsek model which utilises range-based interactions, the topological variant converges to the long-term limiting behaviour with smaller observation windows. Finally, we show that in contrast to the metric model, which exhibits maximal information transfer for the ordered regime, the topological model maintains this maximal information transfer dependent on noise and velocity, rather than the current phase.

Vicsek模型是一种植绒模型，包括最初提出的具有度量交互作用的简单点粒子：粒子与半径内的邻居对齐。后来，引入了拓扑相互作用，以使粒子与其最接近的粒子对齐$ķ$邻居。我们利用拓扑邻居交互作用模拟Vicsek模型，并估计信息理论量与噪声的关系，每个粒子与其邻居对齐的程度的变异性以及群的方向。这些量对于表征相变（如Vicsek模型所展示的相变）非常重要。我们表明，这些数量，互信息和全局转移熵实际上取决于观测时间，并且与利用基于范围的相互作用的规范Vicsek模型相比，拓扑变体收敛到具有较小观测值的长期限制行为视窗。最后，我们表明，与度量模型相反，度量模型显示了有序体制的最大信息传递，