Dynamics of a traveling hole in one-dimensional systems near subcritical bifurcation

Abstract

The dynamical behavior of a traveling hole in a large one-dimensional (1D) system obeying the complex Ginzburg-Landau amplitude equation is studied numerically as a function of parameters near a subcritical bifurcation. After having established the criterion of Benjamin-Feir-Newell (BFN) instability near the weakly inverted bifurcation, five types of dynamical regimes have been distinguished: laminar state and spatiotemporal intermittency regimes below the BFN line. Beyond the BFN line, we have observed a phase turbulence regime with a conserved phase winding number and no phase dislocations, a defect turbulence regime with a nonzero density of defects and, between these two regimes, a weak turbulence has been identified.