Distributed Delay and Desynchronization in a Neural Mass Model
Bibliographic record
Abstract
Abstract. Neural mass models offer a robust mathematical framework for studying the collective behavior of neural populations and their role in brain function and dysfunction. In this work, we consider a neural mass model which consists of a network of an arbitrary number of Wilson–Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time-delayed, excitatory coupling. We extend previous work on this model to include distributed time delays with commonly used kernel distributions: delta function, uniform distribution, and gamma distribution. Focusing on networks which satisfy a constant row sum condition, we show how each eigenvalue of the connectivity matrix may be related to a Hopf bifurcation and that the eigenvalue determines whether the bifurcation leads to synchronized or desynchronized oscillatory behavior. We consider two example networks, one with all real eigenvalues (bidirectional ring) and one with some complex eigenvalues (unidirectional ring). In bidirectional rings, the Hopf curves are organized so that only the synchronized Hopf leads to asymptotically stable behavior. Thus the behavior in the network is always synchronous. In the unidirectional ring networks, however, intersection points of asynchronous and synchronous Hopf curves may occur, resulting in codimension-two Hopf-Hopf bifurcation points. Thus asymptotically stable synchronous and asynchronous limit cycles can occur as well as torus-like solutions which combine synchronous and asynchronous behavior. Increasing the size of the network or a discrete time delay makes these intersection points, and the associated asynchronous behavior, more likely to occur. The effect of distributed time delays is subtle, with some distributions showing asynchronous behavior more likely for small mean delays and less for larger. Numerical approaches are used to confirm the findings, with Hopf bifurcation curves plotted using Wolfram Mathematica. These insights offer a deeper understanding of the mechanisms underlying desynchronization in large networks of oscillators.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".