Self-organized hyperuniformity in a minimal model of population dynamics

Tal Agranov; Natan Wiegenfeld; Omer Karin; Benjamin D. Simons

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arXiv · 2509.08077

Self-organized hyperuniformity in a minimal model of population dynamics

Tal Agranov·Natan Wiegenfeld·Omer Karin·Benjamin D. Simons

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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 towards a critical steady state with divergent individual life time. 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 non-equilibrium 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.

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Tal Agranov, Natan Wiegenfeld, Omer Karin, Benjamin D. Simons. 2025-09-09. Self-organized hyperuniformity in a minimal model of population dynamics. https://arxiv.org/abs/2509.08077

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