Generic Convergence to Periodic Orbits for Monotone Flows with Respect to 2-Cones and Applications to SEIRS Models
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Bibliographic record
Abstract
.We use a general epidemic model, the SEIRS model with a general nonlinear incidence rate, to show how the recently established generic Poincaré–Bendixson theory of flows monotone with respect to a cone of rank 2 can be used to establish the generic convergence to periodic orbits. Our approach to establishing generic convergence to periodic solutions applies to high-dimensional epidemic systems and predator-prey systems, very much like the generic convergence to equilibria in cooperative systems using the classical monotone dynamical systems theory.Keywordsmonotone flowshigh-rank conesgeneric convergence to periodic orbitsMSC codes34C1234C1534K1135B40
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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