Time-delayed models for the effects of toxicants on populations in contaminated aquatic ecosystems
Bibliographic record
Abstract
Ecotoxicological models play a vital role in understanding the influence of toxicants on population dynamics in contaminated aquatic ecosystems. Traditional differential equation models describing interactions between populations and toxicants typically assume instantaneous population growth, overlooking potential time delays associated with reproductive and maturation processes. In this paper, we introduce two models with time delays to investigate the interaction between a population and a toxicant, where the population growth is governed by a delayed logistic equation. We mainly focus on the stability analysis of the steady states of the models. Our findings indicate that high toxicant concentrations result in population extinction, whereas moderate toxicant levels can potentially induce bistability, where the population's fate, whether persistence or extinction, depends on the initial densities of the population and toxicant. Furthermore, both our theoretical analysis and numerical simulations demonstrate that the time delay can lead to the destabilization of the coexistence steady states and the appearance of periodic solutions through Hopf bifurcation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".