Transient spatiotemporal chaos in the complex Ginzburg-Landau equation on long domains

Abstract

Numerical simulations of the complex Ginzburg-Landau equation in one spatial dimension on periodic domains with sufficiently large spatial period reveal persistent chaotic dynamics in large parts of parameter space that extend into the Benjamin-Feir stable regime. This situation changes when nonperiodic boundary conditions are imposed, and in the Benjamin-Feir stable regime chaos takes the form of a long-lived transient decaying to a spatially uniform oscillatory state. The lifetime of the transient has Poisson statistics and no domain length is found sufficient for persistent chaos