Lyapunov Stability Analysis of a Competition Model with Crowding Eects
Bibliographic record
Abstract
The present study is connected to the analysis of a nonlinear system that covered a wide range of mathematical biology in terms of competition, cooperation, and symbiosis interactions between two species. We focus on how populations change their densities when two different species follow the non-symmetric logistic growth laws. We have investigated the stability of the corresponding densities of population, and to control the convergence of solutions by proper choice of interacting constant and periodic parameters. It shows the effect of crowding tolerance on both species. It will show that there exists an infinite number of coexistence solutions if the resource distributions are identical for both populations. If the carrying capacity of the first species exceeds the rest one, then eventually the second population drops down to extinction. The results are presented studying the Lyapunov functional, phase portraits, and in a series of numerical examples. GANIT J. Bangladesh Math. Soc. 40.2 (2020) 95-110
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.002 | 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 teacher head, 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".