Collective behavior based on topological vision

The collective dynamics of active particles with topological vision are investigated. The topological vision, defined as a combination of the visual field and topological neighborhoods, breaks the action-reaction symmetry, thereby indicating that active particles exhibit the nonreciprocal topological interactions. Furthermore, our model considers position-based attractive force, wherein moving particles navigate using instantaneous visual information from neighboring particles within the topological vision, distinct from conventional models based on the velocity-velocity alignment. We demonstrate that the competition between the noise and the nonreciprocal topological interactions results in the emergence of four typical phases: gas phase, ordered phase, nematic bands, and aggregate traveling polar band. Moreover, the nonreciprocal topological interactions impact both anomalous diffusion and ergodicity breaking. Specifically, the weak nonreciprocal topological interactions lead to ergodic subdiffusion, while the strong nonreciprocal topological interactions give rise to nonergodic superdiffusion. These findings provide a theoretical basis for understanding the nonequilibrium collective transport of active particles with topological vision.