From global flocking to local clustering: Interplay between velocity alignment and visual perception of active particles

Abstract

While flocking together, living organisms follow their neighbors. The Vicsek model [T. Vicsek et al., Phys. Rev. Lett. 75, 1226 (1995)] for living systems, where individuals follow their neighbors within a spherically symmetric neighborhood with local velocity alignment rule in the presence of noise, provides a minimal framework to explore their collective dynamics. Associating limited vision angle to an individual provides a minimal description for cognitive perception. This breaks the spherical symmetry of its neighborhood and implements non-reciprocity within the interaction among themselves. Here, we show that in the low noise regime, with decreasing vision angle, the polar order parameter decreases from ≈1 to a much lower value, indicating a transition from a state with global coherent motion of large clusters to a state with small, locally ordered, fragmented clusters. These clusters can spontaneously merge and split among themselves hindering any significant large scale coherent motion in this state. However, we show that at small vision angles, even though the fragmentation restricts formation of larger sized clusters, particles exhibit strong short-range correlations within the small local clusters. In the high-noise regime, as the vision angle decreases, the local ordering observed for full vision angle (spherically symmetric neighborhood) gradually disappears, producing a homogeneous, disordered, steady state. Here, we probe the steady-state properties by analyzing the distributions and spatial correlations of velocities as well as their related fluctuations and also calculate the cluster size distributions for various sets of vision angle and noise strengths. The time evolution of these quantities helps in characterizing the emergence of the corresponding steady states.