Crossover Behaviour of 3-Species Systems with Mutations or Migrations
Bibliographic record
Abstract
We study the ABC model in the cyclic competition (A+B → 2B, B +C → 2C, C +A → 2A) and the neutral drift (A+B → 2B or 2A, B +C → 2C or 2B, C +A → 2A or 2C) versions, with mutations and migrations introduced into the model. When stochastic phenomena are taken into account, there are three distinct regimes in the model. (i) In the “fixation ” regime, the first extinction time scales with the system size N and has an exponential distribution, with an exponent that depends on the mutation/migration probability per particle µ. (ii) In the “diversity ” regime, the order parameter remains nonzero for very long times, and becomes zero only rarely, almost never for large system sizes. (iii) In the critical regime, the first extinction time has a power law distribution with exponent −1. The critical mutation/migration probability scales with system size as N −1. The transition corresponds to a crossover from diffusive behaviour to Gaussian fluctuations about a stable solution. The analytical results are checked against computer simulations of the model. 0 1
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.003 | 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".