Bifurcation, tested two ways
Stationary continuation resolves the local branch direction; selected time evolutions show how the semidiscrete dynamics cross the threshold.
A paper-to-data companion¶
Paper III studies the loss of stability of a positive constant state as the chemotactic sensitivity crosses a critical value. This companion makes the numerical part of that argument inspectable: every reader-facing figure has a frozen vector source, every stationary state is archived, and the release manifest checks the exact paper and code revisions.
01
See the contract¶
Connect the model, branch coefficient, parameter regimes, and numerical scope used in the manuscript.
02
Inspect the evidence¶
Compare the four stationary branches and the two retained time-integration figures.
03
Reproduce the release¶
Verify 780 gates, all file digests, exact source revisions, and the immutable data bundle.
Evidence matrix¶
| Model and parameters | Stationary branch | Finest-mesh coefficient | Additional evidence |
|---|---|---|---|
Non-minimal a=10, beta=0 |
Supercritical | 0.0084220572 |
Near-threshold time evolution |
Non-minimal beta=3 |
Subcritical | -19.64492609 |
Stationary continuation |
Minimal m=gamma=1 |
Supercritical | 1.922366447 |
Fixed-mass stationary continuation |
Minimal m=gamma=2 |
Subcritical | -1.150522206 |
Fixed-mass stationary continuation |
Non-minimal m=2, beta=1, gamma=2 |
Supercritical | — | Near-threshold time evolution |
The stationary coefficients converge at observed order 1.998--2.009 over
N=40,80,160. The full 2-by-2 comparison, raw branch points, profiles, and
indexed state arrays are in the
immutable v1 bundle.
A deliberately narrow claim
These computations validate the stated spatially semidiscrete numerical comparisons. They do not replace the manuscript's continuous-PDE proofs. Superseded fixed-mass and coefficient-seeded trajectories remain in Git as provenance only and are not promoted by this site.
Frozen release¶
Release 1.0.0 pins the stationary generator and simulator, the manuscript numerical-science revision, the immutable public data commit, all figure hashes, and the four coefficient-convergence records. The data and provenance guide explains the archive boundary; the machine-readable manifest enforces it in CI.