Critical fluctuations of noisy period-doubling maps

TL;DR

This paper derives an exact potential for critical fluctuations in noisy period-doubling maps, revealing universal scaling behaviors and connecting these fluctuations to the Ising model universality class.

Contribution

It extends quasipotential theory to a broad class of period-doubling maps, providing exact potentials for bifurcation fluctuations in the weak noise limit.

Findings

Critical fluctuations follow finite-size mean field theory.

Fluctuations exhibit universal scaling along period-doubling routes.

Static properties align with the Ising model universality class.

Abstract

We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.