Hopf Bifurcation Scenario of a Stochastic Aeroelastic Model with Cubic Nonlinearities
Bibliographic record
Abstract
This paper presents a numerical study of the stochastic Hopf bifurcation of a two-degree-of-freedom noisy aeroelastic system oscillating in pitch and plunge, with a cubic non-linearity in pitch. We consider a mathematical model expressed by a non-linear system of Stratonovich stochastic differential equations. A random dynamical system is associated with this stochastic model, and in this setup a dynamical approach is used to characterize stochastic bifurcation. We use numerical algorithms to estimate the support of the invariant measures and to calculate the Lyapunov exponents. The stochastic Hopf bifurcation corresponds to a change of stability of invariant measures and the occurrence of new invariant measures for the random dynamical system. A stochastic analysis in this case is useful for validating the mathematical model associated with the aeroelastic system.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| 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".