Stability analysis and bifurcations of a modified Nicholson–Bailey type model
Bibliographic record
Abstract
In this paper, we investigate the dynamical behavior of a host-parasite model through the modification of a Nicholson–Bailey (MNB) model that contains four biological parameters in the first closed quadrant. By a re-scaling procedure, the MNB model is then reduced to a two-parameter system that almost entirely carries over the comprehensive dynamics of the original model. The new model always possesses two boundary steady states and we show that a third and unique interior steady state may exist under certain conditions imposed on one of the parameters. We then analyze the local stability of each steady state for a different range of parameters by the linearization process of the model about each steady state. For specific values of the parameters in which a steady state is non-hyperbolic, the stability and dynamics of the steady state are studied by the application of bifurcation identities developed from the center manifold theory. Moreover, using linearized stability function, we find thresholds for which the system is stable or unstable. We eventually study the local stability analysis of a period-doubling bifurcation which may occur once we cross one of these thresholds, implying irregular dynamics which may lead to chaos. The results are supported by some simulations.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".