Moment Lyapunov exponents and stochastic stability of non-linear systems under white-noise excitation
Bibliographic record
Abstract
The moment Lyapunov exponent (MLE) is a critical index for assessing the stochastic stability of structures and has been widely applied to linear systems. However, its application to strongly nonlinear systems remains limited due to the inadequacy of traditional methods, such as the method of stochastic averaging. This paper addresses this gap by analyzing the stochastic stability of strongly nonlinear structural systems subjected to parametric excitations modeled as white noise, using MLEs. The analysis begins with the formulation of a strongly nonlinear system. A stochastic averaging method based on a transformed energy envelope is developed to derive a system of Itô stochastic differential equations. Unlike conventional approaches that rely on the Euclidean norm of the state vector, a modified Khasminskii-type transformation is employed, using the square root of the system's Hamiltonian to study stability. To validate the analytical findings, Monte Carlo simulations are conducted to independently compute the MLE. Additionally, the largest Lyapunov exponents and a stability index are evaluated to further characterize the system's stochastic behavior. The effects of key parameters on stability are systematically investigated. This study offers novel insights into the stochastic dynamics of strongly nonlinear structural systems.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".