ANALYSIS OF HOPF/HOPF BIFURCATIONS IN NONLOCAL HYPERBOLIC MODELS FOR SELF-ORGANISED AGGREGATIONS
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 source (direct Gemma or distilled Codex), 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".