Bifurcation analysis of domain-dependent nonlinear dynamics for a cross-diffusive reaction-diffusion model
Why this work is in the frame
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Bibliographic record
Abstract
Abstract In this work, domain-dependent stability analysis is conducted for a reaction diffusion system with linear cross-diffusion. Its spatiotemporal dynamics are explored for the case of an activator-depleted model of two chemical species in terms of the domain size and its model parameters. Linear stability analysis is employed to derive the constraints which are necessary in understanding the role of linear cross-diffusion in driving the instability of the system. The conditions are proven in terms of lower and upper bounds of the domain size together with the reaction, self and cross-diffusion coefficients. The full parameter classification of the model system is presented in terms of the relationship between the domain size and cross-diffusion-driven instability. Subsequently, regions showing Turing instability, Hopf and transcritical types of bifurcations are demonstrated using the parameter values of the system. Theoretical findings are supported by the finite element simulations on two dimensional rectangular domain. Numerical simulations showing each of the three types of dynamics are examined for the Schnakenberg kinetics, also known as an activator-depleted reaction kinetics.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.002 |
| 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