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Boltzmann approach to collective motion via nonlocal visual interaction

Susumu Ito and Nariya Uchida*

  • *Contact author: uchida@cmpt.phys.tohoku.ac.jp
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Phys. Rev. E 111, 044411 – Published 28 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044411

Abstract

Visual cues play crucial roles in the collective motion of animals, birds, fish, and insects. The interaction mediated by visual information is essentially nonlocal and has many-body nature due to occlusion, which poses a challenging problem in modeling the emergent collective behavior. In this paper, we introduce a Boltzmann-equation approach incorporating nonlocal visual interaction. Occlusion is treated in a self-consistent manner via a coarse-grained density field, which renders the interaction effectively pairwise. Our model also incorporates the recent finding that each organism stochastically selects a neighbor to interact at each instant. We analytically derive the order-disorder transition point, and show that the visual screening effect raises the transition threshold, which does not vanish when the density of the agents or the range of the intrinsic interaction is taken to infinity. Our analysis suggests that the model exhibits a discontinuous transition as in the local interaction models, and but the discontinuity is weakened by the nonlocality. Our study clarifies the essential role of nonlocality in the visual interactions among moving organisms.

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Outline

Information

Phys. Rev. E 111, 044411– Published 28 April, 2025
  • Received 19 August 2024
  • Revised 6 December 2024
  • Accepted 14 April 2025
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