Toxic effects on predator–prey dynamics: From deterministic to stochastic perspectives
Why this work is in the frame
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Bibliographic record
Abstract
This study presents a comprehensive model of predator–prey interactions within a toxic environment, with a particular focus on the effect of toxicant compounds on the development of populations. By incorporating environmental disturbances, the dynamics of the model are investigated to enhance the system’s authenticity. Analytical explanations have been provided for the deterministic system solutions, including positivity, uniform boundedness and persistence. The deterministic portion of the investigation entails a comprehensive examination of occurrence and stability criteria pertaining to every possible equlibria. The bifurcation studies conducted on the system exhibit the appearance of local bifurcations, including transcritical, saddle-node and Hopf bifurcations. Moreover, these evaluations establish the parametric region in which Bautin, Bogdanov–Takens and cusp bifurcation occur. Under a relevant selection of parametric values, the suggested system has the capacity to manifest a wide range of dynamic phenomena, such as bi-stable behavior, emergence of limit cycles, and presence of homoclinic loops. Furthermore, in a stochastic environment, the use of Lyapunov functions explains the existence of a global positive solution. It has additionally been argued that the proposed system exhibits ultimate stochastic boundedness. Subsequently, specific and adequate criteria demonstrate the eradication of both species as well as the long-term survival of prey communities. We have also investigated the impact of the exogenous input rate of toxic substances and the coefficient of toxic substances in both species on the behavior of the whole system, both in deterministic and stochastic scenarios. Theoretical findings have been confirmed by various numerical investigations.
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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 | 0.000 |
| 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 | 0.001 |
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 it