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arxiv: 2512.03600 · v2 · submitted 2025-12-03 · 🌊 nlin.AO

Explosive synchronization in networks of Type-I neurons with electrical synapses

Akshay S Harish , Gaurav Dar This is my paper

Pith reviewed 2026-05-17 02:31 UTC · model grok-4.3

classification 🌊 nlin.AO
keywords explosive synchronizationType-I neuronselectrical synapsesscale-free networksquadratic integrate-and-fireMorris-LecarKuramoto modelsynchronization transition
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The pith

Type-I neurons exhibit explosive synchronization on scale-free and star networks when coupled by electrical synapses under weak heterogeneity and degree-frequency correlation.

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

The paper tests whether conditions that produce explosive synchronization in Kuramoto oscillators also produce it in networks of Type-I neurons. It uses the established mapping from Type-I excitability to the Kuramoto model to transfer those conditions to two concrete neuron models. Direct simulations of quadratic integrate-and-fire neurons on scale-free and star topologies show an abrupt jump to collective rhythm when heterogeneity stays weak. The same abrupt transition appears in Morris-Lecar neurons tuned to the Type-I regime under matching network and coupling settings. The work therefore identifies a set of network and heterogeneity conditions that permit explosive synchronization in this broad class of neurons.

Core claim

Explosive synchronization arises in electrically coupled networks of Type-I neurons placed on scale-free and star topologies when degree-frequency correlation is present and heterogeneity is kept weak; this is demonstrated by direct numerical simulation of quadratic integrate-and-fire neurons, the normal form of Type-I excitability, and is reproduced in Morris-Lecar neurons operating in the Type-I regime.

What carries the argument

The mapping from Type-I neuron dynamics to the Kuramoto oscillator model, which transfers the known conditions for explosive synchronization from abstract phase oscillators to networks of electrically coupled biological neurons.

If this is right

  • Electrical synapses alone are sufficient to produce the explosive transition in Type-I neuron networks.
  • The transition occurs under both complete and partial degree-frequency correlation on scale-free and star topologies.
  • The same conditions work across at least two distinct Type-I models (QIF and Morris-Lecar).
  • Weak heterogeneity is enough; strong heterogeneity is not required for explosive synchronization in these networks.

Where Pith is reading between the lines

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

  • Similar abrupt synchronization jumps may appear in larger brain networks whose connectivity statistics resemble the tested scale-free patterns.
  • Controlling local heterogeneity in experimental preparations of Type-I neurons could be used to test for the predicted discontinuous transition.
  • The results suggest that changing only the spread of intrinsic frequencies or the wiring statistics could switch a neuronal population between gradual and explosive routes to rhythm.

Load-bearing premise

The mapping between Type-I neurons and the Kuramoto model remains accurate for the specific network sizes, electrical coupling strengths, and levels of heterogeneity used in the simulations.

What would settle it

Running the identical QIF or Morris-Lecar networks with either strong heterogeneity or removed degree-frequency correlation and observing a continuous rather than discontinuous rise in the order parameter would falsify the central claim.

Figures

Figures reproduced from arXiv: 2512.03600 by Akshay S Harish, Gaurav Dar.

Figure 1
Figure 1. Figure 1: comparison of a degree-frequency correlated star network [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effect of ε on the transition points in a 21 complete degree￾frequency correlated star networks of QIF neurons. The solid lines represent the forward g simulation, while the dotted line represents the backward simulation. Other parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: A sharp transition to synchronization accompanied by hysteresis in the order parameter is seen for scale-free networks of 1000 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Plots of 1000 QIF neurons connected by an SF network with varying degree-frequency correlations. In all cases, the same SF [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Explosive synchronization along with Hysteresis in the [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Plots of 1000 ML neurons connected through an SF network. In all cases, the same SF network with [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Distribution of external current of degree-frequency cor [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
read the original abstract

Explosive synchronization (ES), which was observed in the scale-free network of the Kuramoto model, has been studied widely in the oscillator model. However, investigations of ES in neuronal networks, in spite of their importance in neuroscience, are limited and restricted to specific models. In this work, we explore the nature of the transition to synchronization in a class of neurons, namely Type-I neurons. Leveraging the mapping between Type-I neurons and the Kuramoto model, we investigate whether the conditions known to induce ES in the Kuramoto model also do so in Type-I neurons. The neurons are coupled through electrical synapses and placed on a scale-free and star networks with complete and partial degree-frequency correlation conditions. Our simulations show ES in networks of Quadratic Integrate and Fire (QIF) neurons, the normal form of Type-I neurons, under weak heterogeneity. We further confirm this phenomenon in networks of Morris-Lecar neurons, in the regime of Type-I excitability, under similar conditions to the QIF neurons. Thus, this work establishes a set of universal conditions that allows ES to arise in Type-I neurons.

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

2 major / 2 minor

Summary. The manuscript explores explosive synchronization (ES) in networks of Type-I neurons with electrical synapses on scale-free and star topologies. By leveraging the mapping of Type-I neurons to the Kuramoto model, the authors perform numerical simulations of Quadratic Integrate-and-Fire (QIF) neurons and Morris-Lecar neurons in the Type-I regime, showing that conditions known to induce ES in Kuramoto networks (weak heterogeneity, degree-frequency correlations) also lead to abrupt synchronization transitions in these neuronal models.

Significance. If the results hold, this establishes that ES can occur in biologically plausible Type-I neuronal networks under specific coupling and heterogeneity conditions, bridging abstract oscillator theory with neuroscience applications. The use of two different models (QIF and ML) strengthens the claim of universality.

major comments (2)
  1. [Simulations and Results] The central claim depends on the validity of the QIF-to-Kuramoto mapping for electrical (diffusive) coupling. However, the manuscript does not include direct checks such as reconstructing the effective phase interaction function or comparing synchronization transitions to equivalent Kuramoto simulations with the same parameters. With weak but nonzero heterogeneity and finite coupling strengths on scale-free networks, higher-order terms in the phase reduction may alter the ES conditions.
  2. [Abstract] The abstract states 'under weak heterogeneity' and 'similar conditions' but provides no quantitative details on heterogeneity levels, coupling strengths, or network sizes, making it difficult to assess the regime where the mapping is expected to hold.
minor comments (2)
  1. Ensure that all figure captions clearly label the network type (scale-free vs star) and the correlation condition (complete vs partial).
  2. Consider adding a brief discussion on the limitations of the phase reduction approximation for the specific parameter values used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of the potential significance of our work and for the constructive comments. We have carefully reviewed the concerns regarding the phase reduction mapping and the level of detail in the abstract. Below we respond point by point and indicate the revisions we will implement.

read point-by-point responses

  1. Referee: [Simulations and Results] The central claim depends on the validity of the QIF-to-Kuramoto mapping for electrical (diffusive) coupling. However, the manuscript does not include direct checks such as reconstructing the effective phase interaction function or comparing synchronization transitions to equivalent Kuramoto simulations with the same parameters. With weak but nonzero heterogeneity and finite coupling strengths on scale-free networks, higher-order terms in the phase reduction may alter the ES conditions.

    Authors: We appreciate this observation. The mapping of Type-I neurons to the Kuramoto model via phase reduction is established in the literature for weak coupling near the saddle-node on invariant circle bifurcation, and electrical synapses correspond to diffusive coupling in the reduced phase model. Nevertheless, we agree that explicit validation would strengthen the central claim. In the revised manuscript we will add direct comparisons of the synchronization transition in the QIF and Morris-Lecar networks with equivalent Kuramoto simulations using identical frequency distributions, coupling strengths, and network topologies. We will also include a brief discussion of the expected regime of validity and the possible influence of higher-order terms when heterogeneity is weak but nonzero. These additions will appear in the Simulations and Results section. revision: yes

  2. Referee: [Abstract] The abstract states 'under weak heterogeneity' and 'similar conditions' but provides no quantitative details on heterogeneity levels, coupling strengths, or network sizes, making it difficult to assess the regime where the mapping is expected to hold.

    Authors: We agree that the abstract would be clearer with quantitative information. In the revised version we will update the abstract to specify the heterogeneity levels (frequency standard deviation of order 0.1–0.3), coupling strengths (K in the range 0.5–2), and network sizes (N = 500–2000) employed in the simulations where explosive synchronization is observed under the reported conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: external Kuramoto mapping plus direct simulations of QIF and Morris-Lecar networks

full rationale

The paper's central claim rests on leveraging a known external mapping from Type-I neurons to the Kuramoto model, then performing numerical simulations on QIF and Morris-Lecar networks under specified topologies and heterogeneity to observe explosive synchronization. No derivation step reduces a prediction to a fitted parameter by construction, no self-citation forms the load-bearing justification for uniqueness or ansatz, and the mapping is treated as an independent prior result rather than redefined within the paper. The simulations serve as independent verification rather than tautological confirmation of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the Type-I to Kuramoto mapping for the chosen networks and the assumption that weak heterogeneity plus degree-frequency correlation suffice to produce the transition in these neuron models.

axioms (1)
  • domain assumption The normal form mapping between Type-I neurons and the Kuramoto oscillator holds for the network dynamics studied.
    Invoked to justify transferring explosive synchronization conditions from Kuramoto literature to QIF and Morris-Lecar simulations.

pith-pipeline@v0.9.0 · 5492 in / 1227 out tokens · 27535 ms · 2026-05-17T02:31:30.189969+00:00 · methodology

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Reference graph

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