ANALYSIS OF HOPF/HOPF BIFURCATIONS IN NONLOCAL HYPERBOLIC MODELS FOR SELF-ORGANISED AGGREGATIONS
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The modelling and investigation of complex spatial and spatio-temporal patterns exhibited by a various self-organised biological aggregations has become one of the most rapidly-expanding research areas. Generally, the majority of the studies in this area either try to reproduce numerically the observed patterns, or use existence results to prove analytically that the models can exhibit certain types of patterns. Here, we focus on a class of nonlocal hyperbolic models for self-organised movement and aggregations, and investigate the bifurcation of some spatial and spatio-temporal patterns observed numerically near a codimension-2 Hopf/Hopf bifurcation point. Using weakly nonlinear analysis and the symmetry of the model, we identify analytically all types of solutions that can exist in the neighbourhood of this bifurcation point. We also discuss the stability of these solutions, and the implication of these stability results on the observed numerical patterns.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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