Explicitly solvable eigenvalue problem and bifurcation delay in sub-diffusive Gierer–Meinhardt model
Bibliographic record
Abstract
A spike solution is constructed on the infinite line for a sub-diffusive version of the Gierer–Meinhardt reaction – diffusion model. A non-local eigenvalue problem governs the spike's stability and is explicitly solvable for a certain choice of the kinetic parameters. Its solution generalises former results for the Gierer–Meinhardt model with regular diffusion, and the normal and anomalous systems' properties are juxtaposed. It is shown that a Hopf bifurcation occurs in the sub-diffusive system for larger values of the time parameter τ o as compared to the normal counterpart, rendering the anomalous system more stable. Asymptotic solutions are obtained near important values of the diffusion anomaly index γ and collectively shown to be valid over most of the applicable range 0 < γ < 1. A bifurcation delay scenario is described for the sub-diffusive system, and the WKB exponent is computed analytically.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".