Basic Mechanisms Driving Complex Spike Dynamics in a Chemotaxis Model with Logistic Growth
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Bibliographic record
Abstract
We investigate the Keller--Segel (KS) model with logistic self-production terms that exhibits complex spatio-temporal dynamics of spikes. These dynamics are driven by merging of spikes on one hand, and spike insertion on the other. In this paper we analyze the basic mechanisms that initiate and sustain these events. We identify two distinguished regimes. In the first regime, a single interior spike drifts toward a boundary. This instability is responsible for spike merging. The same regime further exhibits spike insertion; we identify a fold-point bifurcation which is a precursor to the spike insertion event. In the second regime, we show that it is possible to stabilize a single interior spike, and we compute analytically a critical threshold which is responsible for spike stabilization. In particular, our calculation characterizes a stable spike in the KS model with logistic growth; this is in contrast to the classical KS model, where the interior spike is known to be unstable.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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