Three-frequency motion and chaos in the Ginzburg-Landau equation

Abstract

The Ginzburg-Landau equation with periodic boundary conditions on the interval (0, 2pi/q) is integrated numerically for large times. As q is decreased, the motion in phase space exhibits a sequence of bifurcations from a limit cycle to a two-torus to a three-torus to a choatic regime. The three-torus is observed for a finite range of q and transition to chaotic flow is preceded by frequency locking.