An Organizing Center of Codimension Four in a Predator-Prey Model with Generalist Predator: From Tristability and Quadristability to Transients in a Nonlinear Environmental Change
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Bibliographic record
Abstract
.In this paper, we take the Rosenzweig–MacArthur (RM) model with generalist predator as an example in a constant or changing environment. When the environment is fixed, we provide a more easily verifiable classification, in terms of the coefficients of the system with nilpotent linear part and general higher terms, to determine the types and codimension of nilpotent singularities in a general planar system. Second, by using the existing classification and some algebraic methods, we show that the highest codimension of a nilpotent focus is 4 and the sample RM model with generalist predator can exhibit nilpotent focus bifurcation of codimension 4. Our results indicate that generalist predation can cause not only richer bifurcations and dynamics (such as multitype tristability and quadristability, a figure-eight loop) but also the possible extirpation of prey. When the environment is changing, we study the impact of the rate \(\mu\) and intensity \(\beta\) of a nonlinear environmental change on dynamics. The key observations on the asymptotic and transient dynamics include (i) transient tracking on unstable steady states or oscillations, and transient-related regime shifts; (ii) slow and fast regime shifts; (iii) regulation of transient dynamics by the environmental change parameters \(|\mu |\) and \(\beta\) ; (iv) slow negative or fast positive environmental change can delay or even avoid population extirpation.Keywordsnilpotent focus bifurcation of codimension 4nonlinear environmental changetransient dynamicsregime shiftsquadristabilityMSC codes34C2334D0592Bxx
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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) | 0.001 | 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