Theoretical and numerical approach for quantifying sensitivity to system parameters of nonlinear systems
Bibliographic record
Abstract
Abstract Sensitivity evaluation of nonlinear systems to system parameters is critically important in nonlinear dynamics, though current focuses in the field are mainly on the sensitive dependence of nonlinear systems upon initial conditions. The present research intends to develop an approach for quantitatively measuring the sensitivity of nonlinear dynamic systems to system parameters. A single-value sensitivity index is created via a theoretical approach. Numerical simulations are conducted to demonstrate the reliability and applicability of the index in quantifying and analyzing the system parameter-dependent sensitivity for nonlinear systems. With the implementation of the sensitivity index, a diagram illustrating the sensitive and insensitive regions and degree of sensitivity over a large range of system parameters is constructed for a typical nonlinear dynamic system. The sensitivity index developed shows effectiveness and convenience in quantitatively evaluating and analyzing the parameter-dependent sensitivity for nonlinear systems. The results of the research show that chaos and quasi-periodicity of a nonlinear system are sensitive to the system’s parameters, independent of its sensitivities to initial conditions. Based on the proposed method, region diagrams regarding to different parameters are presented, which may help to avoid high sensitivity parameter values such as stiffness, mass and damping values in the design of mechanical systems.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| 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) | 0.002 | 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".