Re-examination of evidence for low-dimensional chaos in the Canadian Lynx data
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Bibliographic record
Abstract
The time series of the annual number ofCanadian lynx caught by the Hudson Bay company be-tween 1821 and 1935 exhibits pseudo-cyclic behaviour andhas long been considered as an archetypal example of irreg-ularly fluctuating population dynamics. Recently proposedglobal polynomial models of this data have been found toexhibt chaotic dynamics and were therefore presented asdirect evidence of chaos in a real ecosystem. In this pa-per we re-examine that evidence by constructing global ra-dial basis models subject to information theoretic parame-ter constraints. We find that the models exhibit very goodagreement with the data and are able to accurately repro-duce the qualitative long term dynamical behaviour. Themodels also often exhibit “almost” chaotic dynamics, ei-ther: (a) very long period periodicity, (b) a periodic or-bit embedded in a dissipative mixing region, or (c) verylong time transient irregular aperiodic dynamics with anasymptotically periodic orbit. In each case the dynamicsexhibit a very rich range of behaviour and can also pro-vide a qualitatively accurate deterministic model of the ap-parently chaotic dynamics when subjected to a delay re-construction. We conclude that, while the data and thesemodels are consistent with the hypothesis of chaos in a realecosystem, the data may also be adequately explained byperiodic “almost chaotic” behaviour.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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 it