Pseudo-Coherence and Stochastic Synchronization: A Non-Normal Route to Collective Dynamics without Oscillators

TL;DR

This paper introduces pseudo-coherence, a novel mechanism where non-normal stochastic amplification causes collective behavior in stable systems without oscillators, challenging traditional views on synchronization.

Contribution

It reveals how non-normal pseudospectral amplification leads to pseudo-coherence, a new form of collective dynamics in stochastic, non-oscillatory systems, with analytical and minimal model support.

Findings

Pseudo-coherence involves transient phase alignment and broken time-reversal symmetry.

A sharp pseudo-critical transition occurs with increasing non-normality.

Fluctuations concentrate along a dominant mode, producing intermittent order and currents.

Abstract

Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can emerge in stochastic systems that are linearly stable and contain no intrinsic oscillators. The mechanism arises from non-normal pseudospectral amplification and leads to what we term pseudo-coherence: an intermittent form of collective organization characterized by transient phase alignment, broken time-reversal symmetry, positive entropy production, and drifting spectral peaks. Using a minimal overdamped stochastic model, we show that increasing non-normality drives a sharp pseudo-critical transition. Beyond a well-defined threshold, fluctuations concentrate along a dominant reaction mode, generating intermittent growth of Kuramoto-like order parameters and irreversible probability currents without eigenvalue crossings or Hopf bifurcations. Analytically, we demonstrate that pseudo-critical non-normal dynamics reshapes the imaginary pseudospectrum, amplifying slow fluctuations and producing coherent frequency bands under finite-time observation. These results identify pseudo-coherence as a new route to collective temporal organization in non-equilibrium systems, suggesting that apparent rhythms and synchronization in natural systems may arise from non-normal stochastic amplification rather than intrinsic oscillators.