A NEW COMPARISON METHOD FOR STABILITY THEORY OF DIFFERENTIAL SYSTEMS WITH TIME-VARYING DELAYS
Why this work is in the frame
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Bibliographic record
Abstract
In this paper, a new comparison method is developed by using increasing and decreasing mechanisms, which are inherent in time-delay systems, to decompose systems. Based on the new method, whose expected performance is compared with the state of the original system, some new conditions are obtained to guarantee that the original system tracks the expected values. The locally exponential convergence rate and the convergence region of the polynomial differential equations with time-varying delays are also investigated. In particular, the comparison method is used to improve the 3/2 stability theorems of differential systems with pure delays. Moreover, the comparison method is applied to identify a threshold, and to consider the disease-free equilibrium points of an HIV endemic model with stages of progress to AIDs and time-varying delay. It is shown that if the threshold is smaller than 1, the equilibrium point of the model is globally, exponentially stable. Another application of the comparison method is to investigate the global, exponential stability of neural networks, and some new theoretical results are obtained. Numerical simulations are presented to verify the theoretical 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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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