Multistable Phenomena Involving Equilibria and Periodic Motions in Predator–Prey Systems
Bibliographic record
Abstract
In this paper, we consider a number of predator–prey systems with various types of functional responses. Detailed analysis on the dynamics and bifurcations of the systems are given. Particular attention is focused on the complex dynamics due to bifurcation of limit cycles, which may generate bistable or tristable phenomena involving equilibria and oscillating motions. It is shown that predator–prey systems can exhibit such bistable or tristable phenomena due to Hopf bifurcation, giving rise to the coexistence of stable equilibria and stable periodic solutions. Explicit conditions on the system parameters are derived which can be used to determine the number of Hopf bifurcations, the stability of bifurcating limit cycles, and the parameter regime where the bistable or tristable phenomenon occurs. The method developed in this paper can be applied to study certain interesting patterns of complex dynamical behaviors in biological or other physical systems.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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".