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arxiv: 2605.29529 · v1 · pith:KLTFFMO3new · submitted 2026-05-28 · 🌊 nlin.AO · cond-mat.stat-mech· q-bio.NC

Common Noise-Induced Group-Level Synchronization Between Uncoupled Groups of Oscillators

Tae-Wook Ko This is my paper

Pith reviewed 2026-06-28 23:53 UTC · model grok-4.3

classification 🌊 nlin.AO cond-mat.stat-mechq-bio.NC
keywords common noisegroup synchronizationoscillator groupsKuramoto order parameterphase density evolutionuncoupled oscillatorsnoise-induced synchronization
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The pith

Common noise synchronizes the collective oscillations of uncoupled oscillator groups.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that when separate groups of oscillators each receive identical common noise (plus independent local noise), the complex order parameters tracking each group's collective rhythm align over time even though the groups have no coupling between them. This holds for identical oscillators and for nonidentical ones whose natural frequencies are drawn from the same distribution, and whether or not the oscillators within each group are coupled. Numerical simulations reveal fluctuating intra-group synchronization whose order parameters nevertheless track one another; an analytical phase-density evolution mapping explains the mechanism by which the shared noise produces the inter-group alignment.

Core claim

When multiple groups of oscillators are driven by the same common noise, the complex Kuramoto order parameters that represent the collective oscillations of each group synchronize, even in the complete absence of inter-group coupling. This group-level synchronization occurs for both identical oscillators and nonidentical oscillators drawn from identical frequency distributions, and persists with or without intra-group coupling.

What carries the argument

Phase density evolution mapping that tracks how the shared common noise aligns the complex order parameters of uncoupled groups.

If this is right

  • The synchronization of group order parameters occurs without any direct coupling between groups.
  • The effect holds for both identical oscillators and statistically equivalent nonidentical oscillators.
  • Intra-group synchronization levels fluctuate temporally while the order parameters across groups remain aligned.
  • The phase density evolution mapping provides an analytical account of the synchronization observed in simulations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same common-noise mechanism could coordinate activity in biological populations that share an environment but lack direct connections.
  • The result suggests testing whether partial correlation in the common noise still produces measurable group-level alignment.
  • Extensions to larger numbers of groups or to different oscillator models would clarify the robustness of the mapping.

Load-bearing premise

The groups receive exactly identical common noise and, when oscillators are nonidentical, their natural frequencies are drawn from the same distribution so the groups remain statistically equivalent.

What would settle it

Numerical simulations or experiments in which the complex order parameters of the groups fail to align when the groups receive identical common noise.

Figures

Figures reproduced from arXiv: 2605.29529 by Tae-Wook Ko.

Figure 1
Figure 1. Figure 1: FIG. 1. Order parameter [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two groups of uncoupled identical oscillators ( [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Two groups of uncoupled nonidentical oscillators ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Two groups of coupled identical oscillators ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Two groups of coupled nonidentical oscillators ( [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Convergence of phase distributions for two groups o [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. B.2. Two groups of coupled identical oscillators (σω = 0, K > 0) with the same common noise input to the groups (dξ1c = dξ2c) : (a) hR¯i, hσRi, and (b) hrxi as functions of cin. σ = 0.4 and ∆(θ) = 1−cos(θ). Initial conditions are as in [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
read the original abstract

We investigate group-level synchronization between oscillator groups induced by common noise in the absence of inter-group coupling. Each group receives a common noise shared by all its oscillators and independent local noise inputs to individual oscillators. The same common noise is applied to all groups. The system is studied with both identical and nonidentical oscillators, and with and without intra-group coupling. In the nonidentical case, natural frequencies are drawn from the same distribution for both groups, making them statistically equivalent. Through numerical simulations of this system, we find that the degree of synchronization within each group, measured by the absolute value of a complex Kuramoto order parameter, typically shows significant temporal fluctuations. Importantly, the complex order parameters representing the collective oscillations of the groups synchronize when the groups are driven by the same common noise. By deriving a phase density evolution mapping, we analytically explain how this group-level synchronization is achieved in the absence of intra-group coupling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript claims that common noise shared across multiple uncoupled groups of oscillators induces synchronization between the groups' collective dynamics, as quantified by the complex Kuramoto order parameters of each group. This occurs for both identical and nonidentical oscillators (with natural frequencies drawn from the same distribution) and holds with or without intra-group coupling. The result is supported by numerical simulations showing temporal fluctuations in intra-group synchronization but coincidence of inter-group order parameters under identical common noise, together with an analytical phase-density evolution mapping that explains the effect in the large-N limit by showing identical evolution of the groups' phase densities.

Significance. If the central claim holds, the work identifies a purely noise-driven mechanism for group-level synchronization without inter-group coupling or parameter tuning, which is relevant to collective phenomena in systems such as neural populations or coupled oscillators subject to environmental fluctuations. The combination of direct simulations across multiple regimes and the analytical phase-density mapping provides both empirical support and a mechanistic explanation; the setup is free of ad-hoc parameters and relies on the explicit statistical equivalence of the groups.

minor comments (3)
  1. The phase-density mapping is central to the analytical explanation; the manuscript should include the explicit form of the mapping (e.g., the integro-differential equation for the density) and the steps showing that the complex order parameters coincide when the common noise is identical.
  2. Figure captions and axis labels should explicitly state the value of N used in each panel and whether the plotted order-parameter trajectories are single realizations or ensemble averages.
  3. The manuscript cites the standard Kuramoto order parameter but does not reference prior work on common-noise synchronization in oscillator populations; adding 1-2 relevant citations would clarify the novelty.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary and significance assessment of our work on common noise-induced group-level synchronization. We appreciate the recommendation for minor revision and the recognition that the combination of simulations and the phase-density mapping provides both empirical and analytical support.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's derivation begins from the standard phase equations for oscillators driven by shared common noise plus independent local noise, then obtains the phase-density evolution (a continuity/Fokker-Planck equation) under the explicit modeling assumption that both groups receive identical common noise and draw frequencies from the same distribution. The resulting identity of the two density equations directly implies coincidence of their order parameters in the large-N limit; this is a symmetry consequence of the input setup rather than a redefinition or a fitted quantity renamed as a prediction. No self-citation chain, uniqueness theorem, or ansatz imported from prior work by the same authors is invoked to close the argument. The numerical simulations serve only as confirmation of the analytically derived mapping. The derivation is therefore self-contained against the model equations themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted or verified.

pith-pipeline@v0.9.1-grok · 5688 in / 937 out tokens · 24322 ms · 2026-06-28T23:53:18.120062+00:00 · methodology

discussion (0)

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