Bibliographic record
Abstract
The response of nonlinear systems with slow variation of a parameter through a bifurcation may be critically affected by very-low-level noise. Examples to be discussed include passage through resonance of a periodically pumped laser, a transcritical bifurcation associated with a coupled pitch/roll model of ship motion, and a period-doubling cascade of a discrete map. In each case the original form of the response persists as the control parameter varies through the bifurcation, even though this original form is now unstable. Noise is required to trigger the bifurcated form; then there is a rapid transition with exponential growth from one form of response to another. Sinusoidal parameter variation through the bifurcation at sufficiently high frequency may effectively stabilize the original form by preventing an appreciable growth of the bifurcated form; noise is destabilizing. The two competing effects are analyzed using matched-asymptotic-expansions. The innermost of a nested set of three expansions describes how noise causes the growth of the bifurcating form from the original unstable form. Previous results for period-doubling [H. G. Davies and K. Rangavajhula, Proc R. Soc. London, Ser. A 457, 2965–2982 (2001)] are modified for the other types of bifurcation, and are extended to a higher order period-doubling cascade using renormalization.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".