Stability analysis and estimate of the region of attraction of a human respiratory model
Bibliographic record
Abstract
In this paper, we complete the stability analysis of various human respiratory non-linear time delay models introduced in Vielle & Chauvet (1998, Delay equation analysis of human respiratory stability. Math. Biosci., 152, 105–122), Kollár & Turi (2004, Numerical stability analysis in respiratory control system models. Conference on Differential Equations and Applications in Mathematical Biology, Nanaimo, BC, Canada, pp. 65–78), Batzel & Tran (2000a, Stability of the human respiratory control system. Part I: analysis of two-dimensional delay state-space model. J. Math. Biol., 41, 45–79) and Batzel & Tran (2000b, Stability analysis of the human respiratory control system. Part II: analysis of three-dimensional delay state-space model. J. Math. Biol., 41, 80–102). More precisely, we present a detailed mathematical analysis of the stability of the non-linear model trivial equilibrium, an estimate of its region of attraction and exponential estimates of the solutions starting in this region. The proposed approach is constructive and it is based on the use of Lyapunov–Krasovskii functionals of complete type for time-delay systems with a cross term in the time derivative.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 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".