Complex Ginzburg-Landau Equation

Dissipative Solitons · Spiral Waves · Defect Turbulence

Simulation Controls

CGLE Parameters

∂A/∂t = A + (1+ib)∇²A − (1+ic)|A|²A
0.2
3.0
0.03
phase

Parameter Regimes

Frozen solitons: |bc| < 1 + b² (Benjamin-Feir stable)
Spiral waves: dominant near bc ≈ 1
Breathing: amplitude oscillates
Defect turbulence: bc > 1 (BF unstable)
Benjamin-Feir criterion: 1 + bc < 0
Current: bc = 0.6
BF stable: Yes

Amplitude Profile

Physics Notes

CGLE: universal near Hopf bifurcation
A = complex amplitude of oscillation
b = linear dispersion coefficient
c = nonlinear frequency shift
Spiral wave = phase singularity (topological defect)
Winding number ±1 — cannot be destroyed alone
Applications: BZ reaction, cardiac tissue, optics