Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances

Yuzuru Sato; Isaia Nisoli

Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances

Chaotic Dynamics 2026-07-21 v1 Dynamical Systems

Authors: Yuzuru Sato , Isaia Nisoli

Abstract

Noise-induced order (NIO) is a paradigmatic example of nontrivial noise-induced phenomena, characterized by pronounced spectral peaks and pseudoperiodic dynamics. We show that this periodicity is governed by the Ruelle-Pollicott resonances of the annealed transfer operator, independently of dynamical stability. Exact results for an analytically solvable model and numerical results for a modified Lasota--Mackey map show excellent agreement between resonance-based predictions and empirical power spectra across a broad range of noise amplitudes. Independent transitions in stability, diagnosed by the Lyapunov exponent, and statistical periodicity, diagnosed by the Ruelle-Pollicott resonances, give rise to three distinct types of NIO.

Keywords

noise-induced order Ruelle-Pollicott resonances annealed transfer operator power spectrum Lyapunov exponent pseudoperiodic dynamics

Cite

@article{arxiv.2607.18771,
  title  = {Statistical periodicity in noise-induced order from Ruelle-Pollicott resonances},
  author = {Yuzuru Sato and Isaia Nisoli},
  journal= {arXiv preprint arXiv:2607.18771},
  year   = {2026}
}