Abstract: Spatiotemporal behavior of complicated systems in small system size are different from that in big system size. Spatiotemporal behavior in one-dimensional complex Ginzburg-Landau equation is investigation whenthe system size is small. When the system size is increasing, CGLE undergoes vibration solution, standing waves, quasi-periodic states, intermittency. The system size at transition point which the first Hopf bifurcation takes place is analyzed by linear stability analysis. Quasi-periodic states are studied, confirmed to be double frequency spatiotemporal quasi-periodic states.

Key words: complex Ginzbury-Landau equation, Hopf bifurcation, quasi-period