An innovative approach for identifying boundaries of a basin of attraction for a dynamical system using Monte Carlo techniques and Lyapunov exponents
Bibliographic record
Abstract
Stability analysis of nonlinear dynamical systems involves identifying the basins of attraction (BoA) of attractors which is a challenging task. The research on this topic can be categorized into three groups: Non-Lyapunov-based, Lyapunov-function-based, and Lyapunov-exponents-based methods. Non-Lyapunov-based methods have low computational load, but their predictability is low. Lyapunov-function-based methods have strong mathematical background, but not only are not exclusive about the BoA, but also are not feasible for most of the real world applications. Lyapunov-exponents-based methods are capable of performing the task for highly complex systems. However, their computational load is high. In this paper a novel approach is introduced which employs Lyapunov exponents, to benefit from its advantages, and Monte Carlo techniques to reduce the load of computations. The method is demonstrated by two illustrative examples.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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".