Pseudo-coherence and stochastic synchronization: A non-normal route to collective dynamics without oscillators

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, contain no intrinsic oscillators and whose drift operator has strictly real eigenvalues. This domain of the operator space is complementary to the well-studied non-normal quasi-cycle programme, in which the linearized drift already carries a complex pair and non-normality merely widens an existing spectral peak. 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 Andronov–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. A nonlinear stress test of the stochastic Wilson-Cowan and Lotka–Volterra models confirms that the same canonical spectral peak persists even when the imaginary part of the local Jacobian is only intermittent, that is, in regimes where the conditions for a stable quasi-cycle ridge are not satisfied. 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.