Propagation dynamics of two species competition models in a periodic discrete habitat
Bibliographic record
Abstract
Spreading speeds and traveling waves are essential in qualitative studying biological invasions. Sometimes, the invading species can lead to the extinction of the local species competing for resources, and such a phenomenon is called competition exclusion. In this thesis, we study the propagation dynamics of a Lotka-Volterra competition model in a periodic discrete habitat when competition exclusion occurs. First, we present general results on spreading speeds and traveling waves for monotone systems in a periodic discrete habitat. Under appropriate assumptions, we show that a semi-trivial equilibrium is globally stable for the spatially periodic initial value problem when competition exclusion happens. Then we establish the existence of the right ward spreading speed and its coincidence with the minimal wave speed for the spatially periodic right ward traveling waves. We obtain sufficient conditions for the linear determinacy of the right ward spreading speed. Ultimately, we apply all these results to a specific model and conduct numerical simulations to investigate the spreading of the two competing species in a periodic habitat.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 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) | 0.002 | 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 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".