Taming turbulence in the complex Ginzburg-Landau equation

Taming turbulence in the complex Ginzburg-Landau equation (CGLE) by using a global feedback control method and choosing traveling-wave solutions as our target state is investigated. The problem of optimal control for the smallest driving strength is studied by systematically comparing the stabilities of all traveling waves. Within the Benjamin-Feir-Newell unstable parameter region (c(2) < -c(1)(-1)), a critical control curve is determined, which is located at c(2) = alpha c(1)(beta), with alpha approximate to -4.0 and beta approximate to -0.87. It characterizes the transition of chosen traveling-wave target state from long wavelength to short one. This finding is of great significance for taming turbulence in the CGLE and some other spatiotemporal systems as well.