Extensive Spatio-Temporal Chaos in Non-reciprocal Flocking

Abstract: Non-reciprocal interactions in active matter gives 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 non-reciprocal 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 Floquet exponents for the unstable chiral state, a positive Lyapunov exponent, a finite correlation and chaotic length and a broad energy spectrum. Our results suggest that complex, turbulent behavior is a generic possibility in any system where particles or fields interact asymmetrically and may have significant implications for understanding how non-reciprocal interactions could drive chaotic, fluid-like behavior in active matter.