Impact of diffusion-driven instability on traveling wave solutions
Bibliographic record
Abstract
Predator-prey interactions are fundamental components of ecological systems, and spatial heterogeneity in the environment significantly influences their dynamics. This study investigates such types of spatially heterogeneous environments using local and nonlocal models. Initially, we scrutinize a local model incorporating the Allee effect and hunting cooperation among predators, laying the groundwork for understanding system dynamics. Subsequently, the nonlocal interaction captures spatial heterogeneity effects, enriching our comprehension of ecosystem dynamics. Significant ecological phenomena, such as the emergence of traveling waves, highlight the complex interactions between predator and prey populations. Extensive numerical simulations explore a range of solution categories including spatiotemporal chaos at low prey diffusion rate, shedding light on the spatial interaction of the prey-predator populations. We have discussed the patterns behind the traveling wave solutions for different parametric combinations and how Turing instability identifies such patterns. Nevertheless, we identify the traveling waves connecting two equilibrium points directly or indirectly through a stable limit cycle or saddle points.
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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 | 0.004 |
| 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 | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".