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arxiv: 2606.21703 · v1 · pith:33OJ7W6Dnew · submitted 2026-06-19 · 🧬 q-bio.NC · math.DS

Delay coordinates synchronization and induces abrupt transition in excitable networks

Bruno R. R. Boaretto , Kalel L. Rossi , Lyle E. Muller , Elbert E. Macau , Roberto C. Budzinski This is my paper

Pith reviewed 2026-06-26 12:31 UTC · model grok-4.3

classification 🧬 q-bio.NC math.DS
keywords time delaysynchronizationexcitable neuronsabrupt transitionnetwork dynamicsneuronal communication
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The pith

Time delays in excitatory neuron connections create self-sustained oscillations that trigger abrupt in-phase synchronization.

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

The paper shows that finite transmission delays in excitatory links between excitable neurons produce self-sustained oscillations that can be out-of-phase or in-phase. Emergence of these oscillations produces an abrupt transition to full in-phase synchronization when connection strength or delay changes by a small amount. The mechanism is the direct interaction between each neuron's excitable response and the delayed incoming signals. The same transition appears across varied connectivities, neuron models, excitation levels, and noise levels.

Core claim

Delays in excitatory connections between excitable neurons coordinate their synchronization patterns by creating self-sustained oscillations that may be out-of-phase or in-phase. The emergence of these oscillations leads to an abrupt, explosive, transition to in-phase synchronized regimes due to small changes in connection strength or time-delay. The mechanism underlying these phenomena is an interaction between the neuron's excitable dynamics and the delay in signal transmission.

What carries the argument

Interaction between the neuron's excitable dynamics and the delay in signal transmission, which generates self-sustained oscillations.

If this is right

  • Small shifts in connection strength or delay produce sudden jumps from partial to full in-phase locking.
  • The oscillations can remain out-of-phase or switch to in-phase depending on the exact delay and strength values.
  • The abrupt transition persists in the presence of noise and across different network topologies and neuron models.

Where Pith is reading between the lines

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

  • The same delay-driven mechanism could produce sudden state switches in larger brain circuits during normal or pathological activity.
  • Analogous explosive synchronization might occur in other delayed excitable systems such as cardiac tissue or chemical reaction networks.
  • Varying delay while holding strength fixed could serve as an experimental test to isolate the contribution of propagation time.

Load-bearing premise

The interaction of excitable neuron response with transmission delays is what generates the self-sustained oscillations and the abrupt synchronization transition.

What would settle it

A network simulation in which all delays are set exactly to zero while keeping connection strengths, topology, and neuron parameters fixed, to check whether the abrupt transition to in-phase synchronization disappears.

Figures

Figures reproduced from arXiv: 2606.21703 by Bruno R. R. Boaretto, Elbert E. Macau, Kalel L. Rossi, Lyle E. Muller, Roberto C. Budzinski.

Figure 1
Figure 1. Figure 1: Delayed connections lead to an abrupt transition to phase synchronization. (a) We define our system on a random network. In this case, we consider a Watts-Strogatz network with N = 100, k = 10, and p = 0.1. (b) Neurons display irregular spiking activity. We numerically integrate the network and compute R (1) as a function of the coupling ε as we increase and decrease ε in a continued manner. (c) Without de… view at source ↗
Figure 2
Figure 2. Figure 2: Abrupt transition occurs for a wide range of delays. We consider the same network as studied in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Delayed coupling coordinates and sustains spiking activity. (a) We consider a simplified network com￾posed of two interacting neurons. Each neuron receives ex￾ternal inputs due to the stochastic noise (D = 0.2) and is also coupled to the other neuron. We consider a fixed value of coupling ε = 0.4, and vary the value of the delay τ . The system is initialized in a synchronized state and integrated for 300 t… view at source ↗
read the original abstract

Neuronal communication is inherently time-delayed, due to the finite speed of signal propagation. Although often considered challenging or disruptive, such time delays can also endow neural circuits with useful capabilities. Here, we show that delays in excitatory connections between excitable neurons coordinate their synchronization patterns by creating self-sustained oscillations that may be out-of-phase or in-phase. The emergence of these oscillations leads to an abrupt, explosive, transition to in-phase synchronized regimes due to small changes in connection strength or time-delay. We describe the mechanism underlying these phenomena as an interaction between the neuron's excitable dynamics and the delay in signal transmission, explaining many aspects of how the oscillations emerge. We show this phenomenon in different network connectivities, neuronal models, with and without excitation, with and without noise, highlighting the generality of the mechanism.

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 / 2 minor

Summary. The manuscript claims that finite time delays in excitatory connections between excitable neurons induce self-sustained oscillations (which can be out-of-phase or in-phase) that coordinate synchronization patterns across the network. These oscillations produce an abrupt, explosive transition to in-phase synchronization triggered by small changes in connection strength or delay. The proposed mechanism is an interaction between the intrinsic excitable dynamics of the neurons and the transmission delay; the authors report that the phenomenon persists across varied connectivities, neuronal models, excitation levels, and noise conditions.

Significance. If the reported mechanism and its generality hold, the result would be significant for the study of collective dynamics in neural circuits. It provides a concrete, delay-based route to explosive synchronization that does not rely on ad-hoc parameter tuning and operates in both deterministic and noisy regimes, offering a plausible explanation for abrupt state transitions observed in biological networks.

minor comments (2)
  1. [Title] The title contains a grammatical error and should be revised for clarity (e.g., 'Delays coordinate synchronization and induce abrupt transitions in excitable networks').
  2. [Abstract] The abstract states that the mechanism is demonstrated 'in different network connectivities, neuronal models, with and without excitation, with and without noise,' but does not name the specific models or connectivities; adding these details would improve reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript on delay-induced synchronization and explosive transitions in excitable networks. The recommendation for minor revision is noted, and we will prepare a revised version accordingly. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claims rest on numerical simulations of excitable neuron networks incorporating time delays, demonstrating self-sustained oscillations and abrupt synchronization transitions across varied connectivities, models, excitation levels, and noise. The described mechanism (interaction of excitable dynamics with transmission delays) is presented as an explanatory account of the observed simulation outcomes rather than a mathematical derivation that reduces to fitted parameters or self-citations by construction. No equations, uniqueness theorems, or ansatzes are quoted that would indicate self-definitional or load-bearing circular steps; the generality is established empirically.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no information on free parameters, axioms, or invented entities is provided.

pith-pipeline@v0.9.1-grok · 5690 in / 1124 out tokens · 54345 ms · 2026-06-26T12:31:10.909337+00:00 · methodology

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