paper · 15 June 2026

Rosetta Stone of Neural Mass Models

Castaldo, de Palma Aristides, Clusella, Garcia-Ojalvo, Ruffini — Physics Reports 1189, 2026.

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Castaldo, de Palma Aristides, Clusella, Garcia-Ojalvo, Ruffini — Physics Reports 1189, 2026.

Why I cared. If you want to model brain rhythms, you reach for a neural mass model — but there are dozens of them, scattered across traditions that barely talk to each other: lumped-parameter models, firing-rate equations, multi-layer generators. Choosing one felt like a subjective act, almost a matter of taste. That bothered me. I wanted the choice to be a principled design decision instead.

What I did. I started from the simplest thing that oscillates — an undamped harmonic oscillator — and the simplest reason a brain does: a push–pull between excitatory and inhibitory populations. From there I climbed a ladder of detail, one rung at a time. Each model appears three times: alone, then under forcing, then wired into a network — which is also the path from a single node to a whole brain. Laid out that way, formalisms that looked unrelated turn out to be neighbours on a continuum of abstraction.

PHASE SPACE BIFURCATION Phase-onlyoscillatora)Dampedoscillatorb)Stuart–Landauc)Wilson–Cowand)NMM1(Jansen–Rit)e)NMM2(ING)f) Model Complexity
Oscillatory dynamics across increasing model complexity — phase portraits (top, integrated from each model's equations) and bifurcations (bottom), from a phase-only oscillator to the ING neural mass model.

What I found. The zoo isn’t a zoo; it’s a ladder. The same dynamical language runs underneath all of these models, and once you can see the rungs you can translate between scales, modalities, and interventions instead of starting over each time. A Rosetta Stone — a shared grammar that still keeps the dialect of each model intact.

What it opened. If the models are rungs, which rung does a given experiment actually need — and can the data tell you? Where does the ladder break — what can’t be reached by adding detail this way? And does the same translation move cleanly between EEG, MEG and fMRI, or does each modality want its own rung?

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