Bibliographic record
Abstract
Introduction Self Sustaining Oscillators are of interest to researchers given the fact that they provide for excellent test beds to study the nuances and intricacies involved in typical oscillatory systems. Numerous such oscillations have been studied using traditional numerical methods in the past, contrary to the propositions of this article. Majority of study of van der Pol equation like oscillatory systems are directed towards deducing a stability criterion. This paper outlines a non-conventional study of the stability standards of the van der Pol Equation. The equation simulates a typical RLC circuit i.e. as a resistor for higher currents, but as a negative resistor for lower currents. Such a behavior is termed Relaxation Oscillation [Nanjundiah 1958]. The van der Pol equation may be defined as an ODE describing oscillations which amplifies smaller oscillations and dampens large oscillations on the other side. It may be obtained by differentiating the Rayleigh Equation and setting y = y’. Detailed analysis of van der Pol equation and its applicability may be found in [Wiggins 1990, Buonomo 1999, Kneubuehl and Kneubhyl 2001]. One of prevalent forms of the van der Pol equation may be given as [Buonomo 1999, Kneubuehl and Kneubhyl 2001]; y” – μ (1 – y) y’ + y = 0 (0)
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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 | 0.006 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.010 |
| Scholarly communication | 0.006 | 0.012 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.022 | 0.004 |
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".