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Condensed Matter > Statistical Mechanics
Title: Critical behavior of a phase transition in the dynamics of interacting populations
(Submitted on 7 Feb 2024 (v1), last revised 16 Apr 2024 (this version, v2))
Abstract: Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population sizes reach a fixed point, to a phase where they fluctuate indefinitely. Here we provide a theory for the critical behavior close to the phase transition. We show that timescales diverge at the transition and that temporal fluctuations grow continuously upon crossing it. We further show the existence of three different universality classes, with different sets of critical exponents, depending on the migration rate which couples the system to its surroundings.
Submission history
From: Thibaut Arnoulx De Pirey [view email][v1] Wed, 7 Feb 2024 18:14:55 GMT (853kb,D)
[v2] Tue, 16 Apr 2024 13:31:59 GMT (861kb,D)
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