SciPost Phys. 18, 051 (2025) ·
published 13 February 2025
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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, highlighting the importance of the migration rate coupling the system to its surroundings.
