Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model
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Bibliographic record
Abstract
In recent studies, global Hopf branches were investigated fordelayed model of HTLV-I infection with delay-independent parameters.It is shown in [8,9] that when stability switches occur,global Hopf branches tend to be bounded, and different branches canoverlap to produce coexistence of stable periodic solutions. In thispaper, we investigate global Hopf branches for delayed systems withdelay-dependent parameters. Using a delayed predator-prey model asan example, we demonstrate that stability switches caused by varyingthe time delay are accompanied by bounded global Hopf branches. Whenmultiple Hopf branches exist, they are nested and the overlapproduces coexistence of two or possibly more stable limit cycles.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 it