Existence and stability of sawtooth periodic solutions in a state-dependent switching system
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
In this paper, we investigate the existence and stability of sawtooth periodic solutions of a new scalar switching system with state dependence. We find two threshold regions for the switch, denoted as $ D_M^* $ and $ D_M^{**} $, such that every solution will eventually converge to a constant if the threshold is located in $ D_M^* $, but there exists a unique globally asymptotically stable sawtooth periodic solution if it is located in $ D_M^{**} $ under suitable conditions with the aid of the Poincaré mapping method. Furthermore, the non-existence of sawtooth periodic solutions is investigated through utilizing an ingenious contradiction argument which seems to be the first attempt. As an example, we apply our theory to show the existence of novel forms of sawtooth periodic solutions in a mosquito population suppression model.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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