Dynamics of a pine wilt disease control model with nonlocal competition and memory diffusion
Bibliographic record
Abstract
Pine wilt disease (PWD) is mainly spread by Monochamus alternatus (in short, M. alternatus). Woodpecker, as the natural predator of M. alternatus, is considered for biological prevention and controlling the PWD. In this paper, we propose a new M. alternatus-woodpecker model with nonlocal competition and memory-based diffusion, which makes the model more realistic for the PWD control. We focus on the dynamics and bifurcations of the model with various combinations of the memory diffusion and nonlocal competition. It is shown that the nonlocal competition can only cause the stable constant steady state to lose stability, while the memory-based diffusion can induce unstable spatially inhomogeneous periodic solutions due to Hopf bifurcation. Consequently, we can explain the spatiotemporal heterogeneity problem in ecology by innovatively using mathematical modelling. Normal form theory with the multiple time scales method is applied to particularly consider Hopf bifurcation, showing complex dynamical behaviours involving various oscillating motions. Finally, numerical simulations are presented with the parameter values chosen from the real forest data of Yuan'an County, Hubei Province, China, confirming the theoretical results of the spatiotemporal heterogeneity of forest diseases and pests, as well as the PWD control.
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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) | 0.001 | 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 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 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".