Biological aggregations from spatial memory and nonlocal advection
Bibliographic record
Abstract
We investigate a nonlocal reaction–diffusion–advection model of a population of organisms that integrates spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE–ODE system reflective of several models found in spatial ecology. Our study advances the mathematical understanding of such models by proving the existence and uniqueness of a global weak solution in one spatial dimension using an iterative approach. This result includes potentially discontinuous detection kernels, explicitly emphasizing the so-called ‘top-hat’ detection function, and does not place any restriction on the rate of advection, thereby addressing some analytical voids in the mathematical discourse on such models. A comprehensive spectral and stability analysis is also performed, providing analytical expressions for bifurcation values contingent on various model parameters, such as species advection rate, diffusion rate, memory uptake and decay rates. Unlike classical reaction–diffusion systems, the point spectrum may now include elements that have an infinite-dimensional kernel. We show the existence of such a point and that it remains negative, ensuring that it does not influence the stability of the constant steady state. Linear stability analysis then provides critical values for destabilizing the constant steady state. We explicitly describe the form of the non-constant steady state near these critical values and classify the nature of the pitchfork bifurcation as forward/backward and stable/unstable. To complement our analytical insights, we explore a targeted case study of three particular instances with the top-hat detection function. Using a pseudo-spectral method, we depict a numerical bifurcation diagram showing cases with sub or supercritical behaviour.
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.
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 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".