Validation
The model is evaluated through numerical simulations under different parameter regimes. Selected results are presented below.
---1. Diffusion Dominant Regime
Parameters:
| α | β | γ | δ |
|---|---|---|---|
| 0.2 | 0.0 | 0.0 | 0.0 |
Outcome:
- System converges to uniform state
- No persistent structures observed
2. Non-linear Without Constraint
| α | β | γ | δ |
|---|---|---|---|
| 0.1 | 0.3 | 0.1 | 0.0 |
- Local amplification observed
- No long-term stability
3. Constrained Regime
| α | β | γ | δ |
|---|---|---|---|
| 0.08 | 0.25 | 0.2 | 0.15 |
- Localized structures appear
- Patterns persist over time
4. Rotational Dynamics
| α | β | γ | δ | κ |
|---|---|---|---|---|
| 0.08 | 0.25 | 0.2 | 0.15 | 0.1 |
- Curved and asymmetric structures observed
- Directional behavior emerges
Summary
Across all tested configurations, structure appears only when constraint and non-linearity are both present.
Extended datasets are available in the technical notes section.