Bibliographic record
Abstract
In the study of forced oscillator phenomena, we have avoided plunging into heavy analysis because generally the details can be gory and are probably soon forgotten by the student. The virtue of maps, and the logistic map in particular, is that they are amenable to relatively simple, easily understandable, analysis because they are governed by finite difference equations rather than nonlinear differential equations. Despite their relative simplicity, nonlinear maps can guide us along the road to understanding many of the features that are seen in forced nonlinear oscillator systems such as the period doubling route to chaos, the stretching and folding of strange attractors, and so on. The emphasis will be on understanding rather than trying to establish the direct connection of a given map with a particular nonlinear ODE which is a nontrivial task beyond the scope of this text. Some new concepts like bifurcation diagrams and Lyapunov exponents, which will be encountered in this chapter, could have been introduced in the last chapter but are more easily dealt with in the framework of nonlinear maps. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.024 | 0.010 |
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".