Extensive Spatiotemporal Chaos in Nonreciprocal Flocking

Nonreciprocal interactions in active matter give rise to a multitude of fascinating phenomena among which are collective oscillatory states without intrinsic particle chirality and active turbulence. Here we show that, in a paradigmatic model for nonreciprocal flocking, the two-species Vicsek model, these two states coexist: chiral order for small flocks and extensive spatiotemporal chaos for large flocks, both separated by a finite-wavelength instability whose scale is set by the rotation radius of the chiral orbits. For system sizes larger than this length scale extensive spatiotemporal chaos unfolds, as manifested by an extensive number of positive Lyapunov exponents as well as of Floquet exponents, a finite correlation and chaotic length, and a broad energy spectrum. Our results suggest that complex, turbulent behavior is a generic possibility in systems where particles or fields interact asymmetrically and may have significant implications for understanding how nonreciprocal interactions could drive chaotic, fluidlike behavior in active matter.