Critical diapause portion for oscillations: Parametric trigonometric functions and their applications for Hopf bifurcation analyses
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Bibliographic record
Abstract
An important adaptive mechanism for ticks in respond to variable climate is diapause. Incorporating this physiological mechanism into a tick population dynamics model results in a delay differential system with multiple delays. Here, we consider a mechanistic model that takes into consideration of the development diapause by both larvae and nymph ticks, which share a common set of hosts. We introduce the concept of parametric trigonometric functions (convex combinations of two trigonometric functions with different oscillation frequencies) and explore their qualitative properties to derive an explicit formula of the critical diapause portion for the Hopf bifurcation to take place. Our work shows analytically that diapause can generate complex oscillations even though seasonality is not included.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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