A Predator–Prey Model with Prey Population Guided Anti-Predator Behavior
Bibliographic record
Abstract
We consider a predator–prey system with prey population guided anti-predator behavior, in which anti-predator behaviors happen only when the population size of the prey is greater than a threshold. We investigate the rich dynamics of the proposed piecewise model as well as both subsystems without and with nonlinear functional response. In particular, the subsystem with anti-predator behaviors exhibits rich dynamical behaviors including saddle-node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Further, besides the dynamical properties of subsystems the piecewise system shows some new complicated dynamical behaviors as the threshold value varies, including unstable limit cycle, semistable limit cycle, bistability of equilibrium and limit cycle, and tristability of three equilibria. From the switching system we can conclude that a great anti-predator rate induces the prey population to persist more likely, but whether the prey and predator populations coexist depends further on the threshold that triggers anti-predator behavior. Especially, a large threshold not only makes coexistence of the prey and predator populations as an equilibrium more likely, but also damps the predator–prey oscillations.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| 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".