Complex Ginzburg-Landau — Spiral Defects

Spatiotemporal chaos and spiral wave cores in oscillatory media

The CGLE

The complex Ginzburg-Landau equation governs oscillatory media near a Hopf bifurcation:

∂A/∂t = A + (1+ib)∇²A − (1+ic)|A|²A

A(x,t) is a complex amplitude. Phase defects (spiral cores) form where |A|=0. Colors encode the phase arg(A).

b: diffusion anisotropy
c: nonlinear frequency shift

Benjamin-Feir instability triggers when 1+bc < 0 — plane waves become unstable, spirals proliferate.

BF unstable when 1+bc < 0