Modeling the Dynamics of a Ratio-Dependent Leslie–Gower Predator–Prey System with Strong Allee Effect
Bibliographic record
Abstract
In this paper, the dynamics of a ratio-dependent predator–prey model with strong Allee effect and Holling IV functional response is investigated by using dynamical analysis. The model is shown to have complex dynamical behaviors including subcritical or supercritical Hopf bifurcation, saddle-node bifurcation, Bogdanov–Takens bifurcation of codimension-2, a nilpotent focus or cusp of codimension-2. The codimension-2 Bogdanov–Takens bifurcation point acts as an organizing center for the whole bifurcation set. The coexistence of stable and unstable positive equilibria, homoclinic cycle is also found. Our analysis shows that the ratio-dependent model may collapse suddenly due to certain parameter variation, i.e. the numbers of predator and prey will decrease sharply to zeroes after undergoing a short time of sustained oscillations with small amplitudes. Of particular interest is that the coalescence of saddle-node bifurcation point and Hopf bifurcation point may indicate the occurrence of relaxation oscillations and the critical state of extinction of predator and prey. Numerical simulations and phase portraits including one-parameter bifurcation curve and two-parameter bifurcation curves are given to illustrate the theoretical results.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".