Three-Frequency Motion and Chaos in the Ginzburg-Landau Equation

Abstract

The Ginzburg-Landau equation with periodic boundary conditions on the interval [0, $\frac{2\pi }{q}$] 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 chaotic regime. The three-torus is observed for a finite range of $q$ and transition to chaotic flow is preceded by frequency locking.