Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem
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Bibliographic record
Abstract
We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting.
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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 | 0.000 |
| 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 it