Time-periodic spatial chaos in the complex Ginzburg-Landau equation

The phenomenon of time-periodic evolution of spatial chaos is investigated in the frames of one- and two-dimensional complex Ginzburg-Landau equations. It is found that there exists a region of the parameters in which disordered spatial distribution of the field behaves periodically in time; the boundaries of this region are determined. The transition to the regime of spatiotemporal chaos is investigated and the possibility of describing spatial disorder by a system of ordinary differential equations is analyzed. The effect of the size of the system on the shape and period of oscillations is investigated. It is found that in two-dimensional case the regime of time-periodic spatial disorder arises only in a narrow strip, the critical width of which is estimated. The phenomenon investigated in this paper indicates that a family of limit cycles with finite basins exists in the functional phase space of the complex Ginzburg-Landau equation in finite regions of the parameters