Complex network structure of flocks in the Vicsek Model with Vectorial Noise

Abstract

In the Vicsek Model (VM), self-driven individuals try to adopt the direction of movement of their neighbors under the in°uence of noise, thus leading to a noise-driven order–disorder phase transition. By implementing the so-called Vectorial Noise (VN) variant of the VM (i.e. the VMVN model), this phase transition has been shown to be discontinuous (¯rst-order). In this paper, we perform an extensive complex network study of VM-VN °ocks and show that their topology can be described as highly clustered, assortative, and nonhierarchical. We also study the behavior of the VM-VN model in the case of \frozen °ocks" in which, after the °ocks are formed using the full dynamics, particle displacements are suppressed (i.e. only rotations are allowed). Under this kind of restricted dynamics, we show that VM-VN °ocks are unable to support the ordered phase. Therefore, we conclude that the particle displacements at every time-step in the VM-VN dynamics are a key element needed to sustain long-range ordering throughout.