An Analytical and Numerical Approach to Vegetation–Nutrient Dynamics Involving Symbiotic Nitrogen Fixation and the Allee Effect
Bibliographic record
Abstract
This study develops a nonlinear dynamical system with three variables representing the standardized abundances of a leguminous plant, a non-leguminous plant, and a nutrient resource. The system is governed by a set of nonlinear conformable fractional differential equations without delay. We establish the unique existence of solutions, derive analytical results for special cases, and present a numerical investigation of the agroecological dynamics. The model is grounded in field experiments involving Trifolium repens (clover) and Mentha × piperita (mint) cultivated on both flat and sloped plots. Stable isotope analysis was conducted to semi-quantitatively trace the fate of nitrogen atoms, accounting for isotope fractionation, and to validate the model structure. Leaf area was quantified via image processing, and photometric analysis of soil pore water was used to determine the concentrations of clover, mint, and nitrate-nitrogen. Using repeated least squares estimation, model parameters were calibrated based on observed and normalized variable values. The results indicate a pronounced Allee effect in the interaction between clover and the soil environment.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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".