Bibliographic record
Abstract
The Lotka-Volterra equations are a classical model of the populations of interacting \nspecies. In the case of two interacting species, we present a closed parametric solution \nto a particular case of the Lotka-Volterra model. We also determine closed expressions \nfor the branch points, bounds on the parameter, amplitude of the oscillation of the \nprey and predator populations, and period of this model in terms of the Lambert W \nfunction. In the case of three interacting species, under certain conditions solutions \nare again periodic. However, standard numerical methods often fail to preserve this \nperiodicity, as well as other important properties of the model. The underlying geometry \nof the three-species predator-prey model is developed through the framework of \nPoisson dynamics. It is shown that the system is bi-Poisson and possesses two independent first integrals. Numerical methods for approximating solutions to the model \nare constructed which incorporate the underlying Poisson geometry of the continuous \nsystem. These methods preserve the periodicity of solutions, and the error in the first \nintegrals remains bounded. Simulations are used to show that these methods produce \nmore accurate results than standard numerical methods which do not consider the \nPoisson structure of the equations.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".