Table 2 The onsets of four main classes of instability
From: Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK
Pattern stability | ||||
|---|---|---|---|---|
Bifurcation | Critical wavenumber | Eigenvalue (σ q = α + iω) | Spatially | Temporally |
Turing | q ≠ 0 | σ q = 0 | Unstable | Stable |
Hopf | q = 0 | α = 0, ω ≠ 0 | Stable | Unstable |
Turing–Hopf | q ≥ 0 | α = 0, ω ≠ 0 at q = 0 | Unstable | Unstable |
Wave | q ≠ 0 | α ≥ 0, ω > 0 | Wave instability | |