Propagation dynamics of a time periodic and delayed reaction-diffusion model without quasi-monotonicity
Bibliographic record
Abstract
In this paper, we consider a time periodic non-monotone and nonlocal delayed reaction-diffusion population model with stage structure. We first prove the existence of the asymptotic speed c ∗ c^* of spread by virtue of two auxiliary equations and comparison arguments. By the method of super- and sub-solutions and the fixed point theorem, as applied to the truncated problem on a finite interval, and the limiting arguments, we then establish the existence of time periodic traveling wave solutions of the model system with wave speed c > c ∗ c>c^* . We further use the results of the asymptotic speed of spread to obtain the non-existence of traveling wave solutions for wave speed c > c ∗ c>c^* . Finally, we prove the existence of the critical periodic traveling wave with wave speed c = c ∗ c=c^* . It turns out that the asymptotic speed of spread coincides with the minimal wave speed for positive periodic traveling waves. These results are also applied to the model system with two prototypical birth functions.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".