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Extensive Spatiotemporal Chaos in Nonreciprocal Flocking

Chul-Ung Woo1, Jae Dong Noh1,2, and Heiko Rieger1

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Phys. Rev. Lett. 137, 118301 – Published 8 September, 2026

DOI: https://doi.org/10.1103/lfwy-bbmv

Abstract

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.

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Physics Subject Headings (PhySH)

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Nonreciprocity Sends Flocks into Chaos

Published 8 September, 2026

Two intermingled species of active matter can exhibit coherent rotation or disorderly scrambling depending on their mutual interactions.

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Breakdown of Emergent Chiral Order and Defect Chaos in Nonreciprocal Flocks

Charlotte Myin, Suropriya Saha, and Benoît Mahault
Phys. Rev. Lett. 137, 118302 (2026)

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Phys. Rev. Lett. 137, 118301– Published 8 September, 2026
  • Received 7 April 2026
  • Accepted 24 June 2026
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