Investigation of the Transition Character for Duffing System by Employing Periodicity Ratio and Lyapunov Exponents
Bibliographic record
Abstract
The transition characters from periodicity to chaos and periodicity to quasi-periodicity have been detected for a Duffing equation which is a representative nonlinear dynamic system who has complicated, diverse transition characters. Specifically, Lyapunov exponents and periodicity ratio method are both employed to diagnose the transition routes. By combining the two methods together, it is very efficient to classify different types of transition of a nonlinear differential system. It can be found that the transition routes from periodicity to chaos can be more divergent than other routes from periodicity to quasi-periodicity. Therefore, some predications can be made about the occurrence of the chaos by observing the divergence or convergence of the transition routes. Further more, the new symmetrical transition characters from periodicity to quasi-periodicity can be displayed in terms of the periodicity Ratio. Comparing to Lyapunov Exponents, the Periodicity Ratio can disclose more detailed transition information.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".