Interaction of in-phase and anti-phase synchronies in a coupled compartment-bulk diffusion model at a double Hopf bifurcation
Bibliographic record
Abstract
We study a model of chemical oscillations in two identical compartments, coupled by a chemical signal diffusing and degrading in the 1D bulk medium between the compartments. The nonlinear compartment-bulk diffusion model consists of a coupled system of ordinary and partial differential equations. Previous numerical work on this system reveals the presence of two modes of synchronized oscillations, in-phase and anti-phase, which arise from Hopf bifurcations of the unique steady state of the system. The coincidence of the two Hopf bifurcations indicates a double Hopf bifurcation point. We use centre manifold and normal form theory to reduce the local dynamics of the model system to a system of two amplitude equations, which determines the patterns of Hopf bifurcation and stability of the two modes near the double Hopf point. In the case of bistability, the stable manifold of an unstable invariant torus forms the boundary between the basins of attraction of the stable in-phase and anti-phase modes. Numerical simulations support these predictions.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.001 | 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".