Bifurcation Analysis of a General Discrete Predator–Prey Model with Fear Effect
Bibliographic record
Abstract
This study presents a comprehensive bifurcation analysis of a generalized discrete predator–prey model that incorporates the fear effect, extending previous research by examining the impact of fear on system dynamics through a novel theoretical framework. Initially, we generalize some existing discrete predator–prey models with fear effect, then analyze the dynamical properties such as the existence of the fixed points, the local stability and possible bifurcations for the discrete model. With the aid of bifurcation theory and the central manifold theorem, we provide sufficient conditions for the model to undergo a flip bifurcation and a Neimark–Sacker bifurcation at the positive fixed point by taking the degree of fear as the bifurcation parameter. Furthermore, we establish criteria for the stability of bifurcated periodic orbits and invariant curves. The obtained results substantially extend and improve some existing ones in the literature. Two numerical examples and simulations are given to check the validity of the theoretical results, and to reveal that fear effect has a significant impact on dynamical behaviors of the predator–prey system.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 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) | 0.001 | 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".