Dynamics of patchy vegetation patterns in the two-dimensional generalized Klausmeier model
Bibliographic record
Abstract
We study the dynamical and steady-state behavior of self-organized spatially localized patches or "spots" of vegetation for the Klausmeier reaction-diffusion (RD) system of spatial ecology that models the interaction between surface water and vegetation biomass on a 2-D spatial landscape with a spatially uniform terrain slope gradient. In this context, we develop and implement a hybrid asymptotic-numerical theory to analyze the existence, linear stability, and slow dynamics of multi-spot quasi-equilibrium spot patterns for the Klausmeier model in the singularly perturbed limit where the biomass diffusivity is much smaller than that of the water resource. From the resulting differential-algebraic (DAE) system of ODEs for the spot locations, one primary focus is to analyze how the constant slope gradient influences the steady-state spot configuration. Our second primary focus is to examine bifurcations in quasi-equilibrium multi-spot patterns that are triggered by a slowly varying time-dependent rainfall rate. Many full numerical simulations of the Klausmeier RD system are performed both to illustrate the effect of the terrain slope and rainfall rate on localized spot patterns, as well as to validate the predictions from our hybrid asymptotic-numerical theory.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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".