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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