Periodic Dynamics of a Reaction-Diffusion-Advection Model with Michaelis–Menten Type Harvesting in Heterogeneous Environments
Bibliographic record
Abstract
Abstract. Organisms inhabit streams, rivers, and estuaries where they are constantly subject to drift and overfishing. Consequently, these organisms often confront the risk of extinction. Can a reasonable fishing ban satisfy the human need for sufficient aquatic proteins without depleting fishery resources? We propose a reaction-diffusion-advection model to answer this question. The model consists of two subequations, which are constantly switched to describe closed seasons and open seasons with Michaelis–Menten type harvesting. We define a threshold value [Formula: see text] for the duration of the fishing ban ([Formula: see text]) and establish the relationships between [Formula: see text] and each of the downstream end [Formula: see text], the advection rate [Formula: see text], and the diffusion rate [Formula: see text]. Under certain conditions, the trivial equilibrium point 0 is globally asymptotically stable if [Formula: see text]. When [Formula: see text], we obtain sufficient conditions on the existence of a globally asymptotically stable periodic solution based on the thresholds in all parameter settings. Finally, some discussions on our findings are provided.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".