Global dynamics of a one-predator-two-prey model and its traveling wave solutions
Bibliographic record
Abstract
This work investigates the three species of one-predator-two-prey ecological models in Lotka-Volterra type functional response with or without diffusive terms. Without the diffusive effects and under two essential assumptions, we can generically classify all global dynamics completely. The global asymptotic stabilities of three equilibria are shown analytically in each case. Alternatively, with the diffusive term, we establish the existence of traveling wave solutions by the higher-dimensional shooting method, the Wazewski principle. In particular, there are two critical wave speeds $0<c_2<c_1$. We show the existence of traveling wave solutions with the wave speed $c$ if $c>c_1$ and the non-existence of traveling wave solutions if $0<c<c_2$. Finally, a brief discussion, biological interpretations, and numerical simulations are given.
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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 | 0.000 |
| 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 | 0.000 |
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".