Spreading Phenomena in Integrodifference Equations with Nonmonotone Growth Functions
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Integrodifference equations are discrete-time cousins of reaction-diffusion equations. Like their continuous-time counterparts, they are used to model spreading phenomena in ecology and other sciences. Unlike their continuous-time counterparts, even scalar integrodifference equations can exhibit nonmonotone dynamics. Few authors studied the existence of spreading speeds and traveling waves in the nonmonotone case; previous numerical simulations indicated the existence of traveling two-cycles. Our numerical observations indicate the presence of several spreading speeds and multiple traveling wave profiles in these equations. We generalize the concept of a spreading speed to encompass this situation and prove the existence of such generalized spreading speeds and associated traveling waves in the corresponding second-iterate operator. Our numerical simulations let us conjecture that these spreading speeds could be linearly determined. We prove the existence of bistable traveling waves in a related second-iterate operator. We relate our results to the existence of stacked waves and to dynamical stabilization.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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 it