A Discrete-Time Modified Leslie-Gower Model with Double Allee Effect and Its Stability and Bifurcation Analysis
Bibliographic record
Abstract
Generally, all the models discussed so far are continuous time models. The continuous time models are quite apt at explaining the phenomena they are trying to predict and have known methods to get information from these type of models. But these models are not accurate for the physical systems which are observed over discreet time periods or which have non-continuous phenomena embedded in them, like production of new generation. Some species like salmon have non-overlapping generation characteristics since they have an annual spawning season and are born each year at a certain time. The discrete models are much more apt in describing the nature’s complex dynamics than the continuous models. A discrete-time modified Leslie-Gower system with double Allee effect is studied in this paper. The stability analysis of interior fixed points is performed. Using center manifold theorem it is shown that the system under consideration exhibits period-doubling and Neimark-Sacker bifurcations. The numerical simulations are provided to illustrate the consistency of the theoretical results.
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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".