Spatiotemporal chaos in the one-dimensional complex Ginzburg-Landau equation

Abstract

The dynamical behavior of a large one-dimensional system obeying the cubic complex Ginzburg-Landau equation is studied numerically as a function of parameters near a supercritical bifurcation. Two types of chaotic behavior can be distinguished beyond the Benjamin-Feir instability, a phase turbulence regime with a conserved phase winding number and no phase dislocations (space-time defects), and a defect regime with a nonzero density of defects. The transition between the two can either be continuous or discontinuous (hysteretic), depending on parameters. The spatial decay of the phase correlation function is inferred to be exponential in both regimes, with a sharp decrease of the correlation length upon entering the defect phase. The temporal decay of correlations is exponential in the defect regime.