A Box-Counting Method for Characteristic Diagnosis of Nonlinear Dynamical Systems
Bibliographic record
Abstract
An innovative box-counting method is developed in this research for diagnozing the nonlinear characteristics of dynamical systems. With the method developed, an approach that depicts the evolutionary process on Poincaré maps is established such that the nonlinear dynamical characteristics of the transient and stable process of the system can be graphically and quantitatively identified. A Duffing–van der Pol system is adopted in the research to demonstrate an application of the method. A diagram graphically describing the periodic, quasiperiodic, chaotic, and transient chaotic regions of the system’s responses is constructed based on the method. Furthermore, the nature of different box-point curves is explained based on the topology of chaos and quasiperiodicity. The method developed shows innovation and efficiency in diagnozing nonlinear dynamical systems based on the topological properties of general nonlinear systems.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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) | 0.000 | 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 teacher head, 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".