Critical behavior of a phase transition in the dynamics of interacting populations

TL;DR

This paper develops a theoretical framework to understand the critical behavior of phase transitions in the dynamics of interacting populations, revealing diverging timescales, growing fluctuations, and universality classes based on migration rates.

Contribution

It introduces a theory describing the critical phenomena near the phase transition in ecological population models with random interactions.

Findings

Timescales diverge at the transition

Temporal fluctuations grow continuously across the transition

Three universality classes with distinct critical exponents

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.