Global stability for a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge
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Bibliographic record
Abstract
Abstract In this paper, a nonautonomous reaction-diffusion predator-prey model with modified Leslie–Gower Holling-II schemes and a prey refuge is proposed. Applying the comparison theory of differential equation, sufficient average criteria on the permanence of solutions and the existence of the positive periodic solutions are established. Moreover, the existence region of the positive periodic solutions is an invariant region dependent on t . Then, constructing a suitable Lyapunov function, we obtain sufficient conditions to guarantee the global asymptotic stability of the positive periodic solutions. Finally, we do some numerical simulations to verify our main results and investigate the effect of prey refuge on the dynamics of the system.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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