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Kinetic theory of pattern formation in a generalized multispecies Vicsek model

Eloise Lardet, Letian Chen, and Thibault Bertrand*

  • *Contact author: t.bertrand@imperial.ac.uk
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Phys. Rev. E 114, 034117 – Published 9 September, 2026

DOI: https://doi.org/10.1103/qjl4-wqvx

Abstract

The theoretical understanding of pattern formation in active systems remains a central problem of interest. Heterogeneous flocks made up of multiple species can exhibit a remarkable diversity of collective states that cannot be obtained from single-species models. In this paper, we derive a kinetic theory for multispecies systems of self-propelled particles with (anti)alignment interactions. We summarize the numerical results for the binary system before employing linear stability analysis on the coarse-grained system. We find good agreement between theoretical predictions and particle simulations, and our kinetic theory is able to capture the correct lengthscale in the emergent coexistence phases through a Turing-Hopf instability. Extending the kinetic framework to multispecies systems with cyclic alignment interactions, we recover precisely the same emergent ordering as corresponding simulations of the microscopic model. More generally, our kinetic theory provides an extensible framework for analyzing pattern formation and collective order in multispecies active matter systems.

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See Also

Flocking Beyond One Species: Novel Phase Coexistence in a Generalized Two-Species Vicsek Model

Eloise Lardet, Letian Chen, and Thibault Bertrand
Phys. Rev. Lett. 137, 118303 (2026)

Article Text

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Phys. Rev. E 114, 034117– Published 9 September, 2026
  • Received 23 December 2025
  • Revised 25 May 2026
  • Accepted 9 July 2026
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