COMPLEX GINZBURG–LANDAU

The CGLE governs spatiotemporal dynamics near Hopf bifurcations: oscillating chemical reactions, laser arrays, fluid convection. Spiral waves, turbulence, and frozen states emerge from the same equation.

∂A/∂t = A - (1+ib)|A|²A + (1+ic)∇²A

b (nonlin. freq.) 1.50 c (diffusion disp.) -1.50 Noise 0.02 Speed 2 Random IC Single spiral IC Color: Phase

Benjamin-Feir instability: |1+bc| > 1 → turbulence