From Global Flocking to Local Clustering: Interplay between Velocity Alignment and Visual Perception of Active Particles

Abstract: Collective behavior in biological systems was first captured by the Vicsek model, in which particles align their velocities in the average direction of neighbors, leading to coherent motion and showing an order-disorder transition. However, in many complex environments, the interactions are non-reciprocal, lacking an action-reaction symmetry. Using framework of the Vicsek model, we implement non-reciprocity by restricting interactions to neighbors located inside a finite vision cone, for a particle by limiting its set of interacting neighbors which fall within a vision-cone, providing a minimal description for cognitive perception. Using detailed numerical simulations, we explore the clustering and flocking behavior due to competition between noise and limited visual perception in the presence of alignment interaction. For low noise, with reduction in the vision angle the system shows transition from a global coherent motion to locally ordered small-sized clusters. This behavior is confirmed through the steady-state distributions of velocity components and their fluctuation relative to the global mean. This is also characterized using a polar order-parameter and a two-point velocity correlation function. Interestingly, at small vision angles, particles exhibit strong short-range correlations within clusters even in the absence of any global coherence. Time-evolution of the related correlation functions illustrate the pathways towards the emergence of such structures. The time dependence of the average cluster size and the length-scale calculated from the two-point velocity correlation show scaling behavior and indicate that the emergence of density field clustering is a consequence of the velocity-field coherence. Any kind of ordering and clustering disappear in the limit of high noise and low vision-angle regime.