Pseudo-Coherence and Stochastic Synchronization: A Non-Normal Route to Collective Dynamics without Oscillators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912951560044544 |
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| author | Troude, V. Sornette, D. |
| author_facet | Troude, V. Sornette, D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-Coherence and Stochastic Synchronization: A Non-Normal Route to Collective Dynamics without Oscillators Troude, V. Sornette, D. Adaptation and Self-Organizing Systems Statistical Mechanics Chaotic Dynamics Pattern Formation and Solitons Data Analysis, Statistics and Probability 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. |
| title | Pseudo-Coherence and Stochastic Synchronization: A Non-Normal Route to Collective Dynamics without Oscillators |
| topic | Adaptation and Self-Organizing Systems Statistical Mechanics Chaotic Dynamics Pattern Formation and Solitons Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2603.07206 |