Macroscopic limit cycle via pure noise-induced phase transition

TL;DR

This paper reexamines noise-induced phase transitions using bifurcation analysis of cumulant dynamics, revealing a new route to macroscopic limit cycles in extended systems, confirmed by simulations.

Contribution

It introduces a cumulant dynamics approach to analytically study noise-induced phase transitions and limit cycles in systems where traditional methods fail.

Findings

Identifies a Hopf bifurcation leading to macroscopic limit cycles

Provides an analytical phase diagram for noise-induced transitions

Confirms theoretical predictions with numerical simulations

Abstract

Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition using this approach we investigate patially-extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to find noise induced phase transitions. A new approach based on cumulant dynamics predicts a noise-induced phase transition through a Hopf bifurcation leading to a macroscopic limit cycle motion, which is confirmed by numerical simulation.