Collective behaviors of self-propelled particles with looming-receding induced non-reciprocal interactions

Classical models of collective motion typically rely on metric-based, reciprocal interactions and often neglect the sensory constraints inherent in biological and robotic systems. In this work, we investigate the collective dynamics of self-propelled agents driven by non-reciprocal responses to optical flow cues, specifically the visual looming and receding of neighbors. By establishing a global power-balance framework, we demonstrate that the interplay between active energy injection and vision-induced dissipation governs the emergence of macroscopic order. Our analysis provides theoretical evidence for the existence of a bounded attracting region in phase space that ensures the ultimate boundedness of collective dynamics. Extensive numerical simulations reveal a complex phase diagram featuring distinct flocking, rotational, and disordered behaviors. Notably, we find that increasing the visual safety radius functions as a structural switch. A larger safety threshold suppresses high-density rotational modes by enlarging the effective exclusion zone, thereby forcing the system into a translational flocking state. These results highlight how anisotropic, non-reciprocal visual perception fundamentally reshapes the attractor landscape of active matter and offer new theoretical insights for designing autonomous swarms with minimal sensing capabilities.