Beyond singular perturbation: Improved criteria for slow-fast oscillations
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Bibliographic record
Abstract
Determining the existence of periodic solutions in dynamical systems is often essential, yet becomes increasingly challenging as the number of system parameters grows. Recurrent oscillatory behavior is commonly observed in biological models, especially in disease models involving persistent infections. A classical approach for identifying slow-fast dynamics involves locating slow or critical manifolds via geometric singular perturbation theory; however, this method is not applicable to many systems. In this paper, we propose a new method for detecting the existence of slow-fast dynamics that drive periodic behavior. Then, this method is applied to a three-dimensional SIR model with secondary transmission and conduct a detailed stability and bifurcation analysis to verify the conditions required by the proposed approach. Numerical simulations are provided to support and illustrate the analytical results.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it