Self-Organized Hyperuniformity in a Minimal Model of Population Dynamics.

Authors

Tal Agranov, Natan Wiegenfeld, Omer Karin, Benjamin D Simons

Published in

Physical review letters. Volume 137. Issue 11. Pages 117401. Sep 11, 2026.

Abstract

By generalizing a class of models recently introduced to account for protracted transients in biological systems, we identify a novel mechanism for hyperuniformity. In this model, competition of individuals over a shared resource serves as feedback that can asymptotically guide the population toward a critical steady state with a divergent individual lifetime. We show that, in its spatially extended form, this many-body model exhibits hyperuniform density fluctuations. Through explicit coarse-graining, we develop a hydrodynamic theory that conforms closely with the results of stochastic simulations. Unlike previous models for nonequilibrium hyperuniform states, our model does not exhibit conservation laws, even in the asymptotic regime. Instead, hyperuniformity arises from the divergence of the range of the resource-mediated interactions. These findings may find applications in engineering, cellular population dynamics, and ecology.

PMID:
42789845
Bibliographic data and abstract were imported from PubMed on 26 Sep 2026.

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